Many confuse muscle size with strength. There is a distinct difference. While many people do low weight, high rep workout to gain muscle mass, they are not necessarily very strong. Conversely, some of the thinner athletes you see can move enormous loads because the strength that they have built into their muscle.
What are Strengthening exercises?
According to WebMD, "Strengthening exercises work muscles as they move against resistance. This resistance can come from workout machines, free weights or barbells, elastic bands, water, stairs, hills, cans of vegetables from the pantry -- even your own body weight as you do a pushup."
Why are they important?
Strengthening exercises build a strong core to extremity stability that enables us to do work, defined here as moving objects, without significant risk of injury.
Weight machines and free weights
Many think there is no difference, but I beg to differ. Weight machines follow pre-defined, controlled paths, enabled by the mechanics of the machines themselves. Free weights on the other hand have no pre-defined patterns. In other words, you must control the location and movement of the weight at all times.
Because of this necessity to control the weight, I believe that working with free weights provides advantages over machine training. Typically, free weights require core strength and stabilization, regardless of what you are doing with them. Most machined isolate on a specific muscle group and allow the remainder of your system to "relax".
What are some of the best exercises for adolescents to build strength?
Again, we should emphasize that we are talking about strong muscles, not the space they take up in a room. These exercises will not necessarily make your young athlete look strong. That said, here are a few we recommend:
Running (particularly in hills)
Cycling (hills are best here also
Skill and strength appropriate lifting
Of course, variety is the spice of life, and adolescents get bored with repetition, so mixing things up and keeping it fun is always important.
With adolescents, the focus should not be heaving loads. Always begin light, increasing load gradually, as they show that their technique and body control is advanced enough to justify moving on. Likely, adolescents will see weekly "personal bests" if you follow this method. Don't allow them to make large jumps. Once they life heavier that last time (by a small margin), record that as their new best, and move on.
This will keep them hitting new bests and encourage their development. Work to keep them successful and growing.