The olympic lifts are the snatch and the clean and jerk. They have many variations that include but aren't limited to the hang snatch, hang clean, power snatch, power clean, dumbbell cleans, dumbbell snatches, and many more. They are all very explosive yet technically challenging total body lifts that are designed - in the sports performance world - to increase the athletes power production. More specifically, to increase power production in triple extension (ankle, knee, and hip extension).
Triple Extension
Obviously, this movement is the same movement an athlete goes through when they jump and sprint (a sprint is basically jumping from one leg to another). These movements (especially the snatch) have been shown time and again to produce more power than any other movement you can perform in the weight room.
*Newton, H.; Explosive Lifting for Sports; Human Kinetics; Champagne, IL; 2001; 17.
Given this, the olympic lifts are also very hard to teach and many coaches will say the potential for injury is high. I'm not one of those coaches. For me, it's more like, do I have time to teach them? Some of the kids that come in to see me are maybe just a couple weeks out from their season. For these kids, I'll usually implement a combination of plyometrics, med ball work, and weighted jumps simply because of the fact that I don't have the time to teach them the lifts. On the other hand, if I get an athlete who is in their off season, and we have several months to work on them, of course we will have them olympic lift.
So, do your athletes olympic lift?
It depends...