From another source, an interesting clip on exercises you should AVOID (with a healthy little dose of humor thrown in):
And, now, the same folks balance it out by talking about some exercises you SHOULD do:
Now, full disclosure here: I am not a huge fan of going to the gym. I don't hate it, I have been a member of several gyms over the years, and I have even seen some pretty noteworthy changes in my physique when I stick with a consistent program for a while. But, it's not my favorite form of strength training and conditioning. I like exercises, like they talk about in the second video clip above (during the Gluteus Medius Extension exercise) that can be done in the living room, a park, a hotel room, at poolside, or anywhere you need/want to do your exercises at the time that suits you best. A chin-up bar, like the kind you can install in a doorway at home, is about as fancy as I like to get with my exercise equipment. Maybe a stability pad or some resistance bands. Not much more than that.
Image above is from NHSChoices.com, an excellent place to see their "10 Minute Workout Guides" for a fantastic list of exercises you can do at home.
I also tend towards the approach, in my own training and in the training plans I write for my clients, of doing exercises with lower resistance (maybe just body weight, most of the time) and more repetitions, but also emphasizing that all repetitions are done with extremely good form and attention to detail. I am not looking to build much bulk in my muscles, myself, and instead want to build a functional kind of strength that allows me to do lots and lots of good quality repetitions for extended periods of time. So, no points for mindless repetitions that might cause injury through bad form, just so you can say, "I did 1,000 sit-ups!" especially if 900 of them were sloppy.
I also like anything that is fun. I guess that's why I like mountain biking, trail running, open water swimming, ultimate frisbee, ping pong, tennis, and training/playing with friends. Whatever it is you do and however you decide to do it, if you enjoy the activity you are doing, you will be more likely to keep doing it consistently, you will be more likely to get better at it, and that, in turn, will encourage you to keep doing it some more. So, to contradict myself totally and infuriatingly, if I found some friends who all loved going to the gym and lifting weights, who showed me how to have a blast with it, then I would probably start doing that regularly, too.
The most important thing I hope you take away from all this: Have fun with it!
[For some pretty extreme, but totally fascinating concepts in strength training, there are some interesting "prisoner workouts" out there that take an interesting approach to no-cost/no-equipment/limited-space exercise, such as: http://www.artofmanliness.com/2015/08/05/the-prisoner-workout/]
Well, on to answering the question at the top there, here are some of the most obvious benefits to strength training...
Increased Strength, Muscular Endurance and Power
Seems like a totally obvious thing to say that strength training can increase your strength, muscular endurance and power, but I also want to explain the differences between these terms we often use, sometimes interchangeably, sometimes erroneously. There are some pretty detailed definitions and explanations on the Livestrong web site that are very useful, but here are my own explanations of the differences amongst these three terms above, and how they might apply to your triathlon training:
Strength is the capacity for a muscle or group of muscles to exert force for one repetition of an action at or near maximal effort. So, obviously, strength training is any kind of training that makes you more able to exert more force through one specific action.
You can train for improvements in strength in lots of different ways. For example, with functional training: jumping a certain height and then jumping higher and higher; or jumping up with both legs and then jumping with one leg at a time, trying to jump higher and higher; or jumping up to the same height but carrying more weight over time. With weight training: mimicking an abstracted movement of the jumping by identifying the muscles and groups involved and then engaging them with weights at the gym (some kind of leg press perhaps).
An example of applied strength, in triathlon fitness terms, might be when you push off the wall at the swimming pool, with one powerful movement. If you build strength in those leg muscles, then you will be able to push stronger and farther over time, for that one motion of a near-maximal effort. This is usually a very trainable aspect of your fitness, where you can see dramatic improvements in relatively short periods of time (typically, a few weeks of consistent training), and it is very easy to measure progress and maintain fitness in this area. Although, it is arguably the most limited type of strength training (I meant, it refers to just one repetition, really).
Muscular Endurance is the capacity for a muscle or group of muscles to exert the same force over several repetitions. This is an aspect of fitness that is extremely important to triathletes and endurance athletes, as you can imagine. It is one thing to be able to say, "I can push 200kg with my legs, once," (an example of strength), and then it is something completely different to be able to say, "I can push 100kg with my legs, 100 times in steady, consistent repetitions." This would be important, say, if you wanted to be able to climb hills on the bike better.
Muscular endurance is a little more difficult to measure than simple strength, but not all that difficult. If you train with a training plan and are in the habit of writing down your work-outs, then it can be easier. For example, if you do a certain warm-up or strength training exercises at regular intervals (e.g. lunges three times a week), then you will be recording how many of each exercise you can do before you reach the point of feeling muscular breakdown, and notice changes over time. If you are consistent in your training, you should see that you can do more and more lunges each week, which means you are experiencing an increase in muscular endurance (assuming, of course, that your body weight stays the same, which it might well not be, but that is a more complicated calculation, so let's just keep it simple for now and ignore that part).
Power is the ability for you to exert a certain force in sustained repetitions, over a given period of time. So, for example, it is one thing to say, "I can keep pedaling consistently in that high gear for 100 revolutions, or about 1km," (an example of muscular endurance), and it is another thing to say, "I can pedal in that high gear consistently at the same cadence [pedal rate] for one hour without slowing down."
This is one of the more complex aspects of fitness that involves adaptations in the amount of force you can exert, for a certain number of repetitions, in a certain amount of time.
We can apply the same principles to any of your sports training, but it is on the bike where it has perhaps become the easiest to measure, with the increasing use of power meters, and the incremental nature of using gears on the bike. For example:
Being able to push a certain hard gear for a certain number of repetitions, in faster and faster times over a month (e.g. you started out pedaling in that high gear for 1,000 revolutions and it took you 15 minutes, and by the end of the month it took you 12 minutes), would be an indication of increase in your power on the bike.
Being able to push increasingly harder gears for a certain number of repetitions, in the same amount of time (e.g. week after week, you are able to push one gear harder each week for a sustained 15 minute work-out, at a consistent cadence throughout), would be an indication of increases in your power on the bike, too.
Being able to push the same hard gear, at the same cadence, for increasingly longer periods of time, would also be an indication of increases in power on the bike.
If I am going to use equipment for strength training myself, or if I am going to recommend any equipment to anyone out there, I think it has to be:
I have been collecting strength training equipment over time, and here are some of my favorites (and, I need to point out that the links I am providing below are not in any way a recommendation for buying things from any one shop or for an endorsement of any one product; the links are provided here merely for illustrating the general nature of the equipment I am talking about):
Chin-up bar. This is a pretty old-school favorite of mine, pretty inexpensive and easy to use. You can get the one (like in the link here) which expands with a heavy spring-and-screw action, to fit into your doorway, or you can also get one that doesn't need to be fitted to your doorway and is therefore more movable. I have always liked having a chin-up bar hanging somewhere in my flat to remind me to do perhaps 4 or 5 chin-ups every time I go past that place - it's a great way to incorporate some useful strength training pretty seamlessly into your daily life! I also like that there are a variety of exercises you can do with chin-up bars that are not just for arms, shoulders, and back (lifting up the legs in various ways while hanging from the chin-up bar is AMAZING strength training for your core).
The other big advantage is that it can be used in conjunction with the next item...
Suspension straps. These are incredibly versatile, very easy to pack with you if you are traveling, and can provide a pretty handy total-body exercise system in one kit. You can attach them to a chin-up bar, for the greatest range of flexibility, but you can also hang them over a door and anchor them that way. I really love these guys and use them pretty regularly myself. Great for arms, great for core, great for legs, and they even provide a kind of instability that very nearly mimics the benefits of the next two items...
Stability pads. These are very flexible and reasonably portable. A small stability pad can be used in so many different ways, and it has been proven that it accelerates your muscular engagement when you stand on an unstable surface while engaging in any exercise.
Stability ball. These follow the same principle as the stability, but being larger, they can be used for a much wider range of activities that includes the whole body. Put your arms on the ball while doing planks and you engage so much more than just doing straight planks. Sit on the ball while doing sit-ups and you turbo-charge your sit-ups. Put your feet on the ball while doing glute bridges, perhaps accompanied by hamstring flexion, and you have an extremely powerful tool for developing a wide range of muscles in each exercise. Of course, the larger size that makes it a much more versatile exercise tool also makes it a much less portable one. I mean, I live in a one-bedroom flat in London, and I don't actually have enough room to keep a stability ball in my flat inflated all the time, so this might be one good reason to go into a gym, if only to use their stability balls...