Pyramid training helps build functional strength, and also prepares a trainee for heavier lifting, as in the case of power-lifting. Coined 'The Weider Principles', Joe Weider, longtime fitness mogul and founder of the famed Mr. Olympia bodybuilding competition, popularized this form of training (primarily through his prodigy Arnold Schwarzenegger) decades ago. But in truth, it's probably been around for much longer than that. In fact, many who have never heard of pyramid training or the Weider principles have discovered it on their own (through trial & error, and/or individual common sense).
Pyramid training is a very natural way of progressing through your workouts, at least in terms of the amount of weight used with each consecutive set. The reason is simple; In any given set of a resistance exercise, the number of repetitions (consisting of both concentric and eccentric movement) will decrease as you move forward (i.e. increase poundage); This, of course, is if you're performing the maximum number of repetitions within each set. Therefore, instead of things getting more difficult all around, there is an ease of tension with regards to at least one major aspect of your training.
The last paragraph indirectly summed up what pyramid training is, but to elaborate, it can be defined as the performing of weight training exercises (usually traditional bodybuilding ones, like 'bench press' for example), starting with lighter weights and higher reps for the first set of each exercise - and reversing this process with each consecutive set. Typically, beginners will perform approximately 3 sets for a single exercise, while intermediate and advanced trainees will perform a higher number of sets (usually within the range of 4-6); They'll also perform more exercises per muscle group in general.
In muscle gyms, or any kind of gym for that matter, pyramid training is used primarily for the purpose of hypertrophy (i.e. building muscle); It's, therefore, incredibly popular amongst bodybuilders, power-lifters, and every other type of athlete involved in some kind of strength sport. A great side-effect of pyramid training (when complemented with proper nutrition, adequate amounts of rest, and a few other factors) is consistent increases in functional strength.
Pyramid training definitely increases functional strength, or in other words, everyday "usable" strength. Because a trainee will perform at least three sets of an exercise for it to be considered pyramid training, contrary to only one extremely heavy set (which is common to power-lifting), it sort of emulates a person's daily actions where physical strength is required. If you live a sedentary lifestyle, possibly work in an office, more often than not hire others to take care of home maintenance & chores, etc... then the benefits received from pyramid training at the local fitness center (or your home gym) are limited to personal health and appearance.
So who can use pyramid training to their advantage? Almost anybody. Also, age is typically not an issue. Teens, seniors, and nearly everyone in between are able to increase functional strength at an impressive rate through this method of working out. As all things in life, it's important to not overdo it, and to be respectful of your limits - but that aside, pyramid training is a really fun way to get strong... and apply that strength both inside and outside of the gym.