Weightlifting is a very technical sport. Much like golf, if you want to get better at snatch and clean and jerk, you have to do both of those things more to master proficiency. However, there are some other qualities that can help us express our technical proficiency to lift more weight on the bar.
One of those qualities is power output. Weightlifting, aside from being a technical sport, is a very explosive sport. It stands to reason that if an athlete can become more explosive, their Olympic lifts will improve, all else being equal.
The one way we improve power output in our programming is through plyometrics. Another word for jumps, throws, and even sprints. Whatever the drill or exercise, the main objective is to produce as much force as possible in the shortest amount of time as possible.
Below are a few reasons how plyometrics can be beneficial to a Weightlifter.
Increased Power
This one might seem a bit obvious. The more you do plyometrics the more likely you are to see increases in power output. That is, if you are programming them intelligently. If you take someone's vertical jump, and put them on a properly periodized and progressive jump program you will see that vertical jump go up in at least two months. This doesn't have to be an extensive jump program, but 10 minutes during your warm-up before your Olympic lifting training session will do. I would bet a decent amount of dollars that you will see increases in vertical jump height for someone that hasn't added the plyometrics into their program previously.
Now, everyone is different and has a certain genetic potential they can reach when it comes to speed and power output. Some people are just born with an ability to jump high while others are born without that ability. However, everyone has a window of potential that they can increase by training. You can be someone who is nothing but slow-twitch, but you can still make increases in power if you train hard and smart. You just might not be that someone who gets from a 30" vertical to a 40."
Lastly, it stands to reason if you can increase a measure like vertical jump height, this increased quality is likely to transfer over, even if it is a little, to the sport of Weightlifting.
Increased Elasticity
There is a little bit more to gain from plyometrics than just raw power output. Power output really only tests whether you can produce a lot of force in a short period of time in one direction. But, something like a vertical jump doesn't tell you how well you can change direction.
When I am talking about elasticity here, I am talking about the ability to change direction, or the ability for your muscles to go from a state of contraction (or force output), to a state one might call "relaxation" (no force output), and then be able to contract again. An example would be a hurdle hop. You have to produce force to jump over the hurdle, but then you have to be able to relax so when you hit the ground again your muscles can contract and spring you back up over the next hurdle. In this example, if you didn't possess the ability to "relax" your muscles after the first jump you wouldn't be able to spring back up, and you would continue to move towards the floor. Muscles have to relax, or yield a little bit in order for the force to be able to be distributed through the muscles and therefore the entire system.
This has some relation to getting under the bar in Weightlifting. If someone doesn't have the ability to yield or relax after producing high force, they might not be one who can get under the bar fast. Driving the bar up on Olympic lifts is about producing force, but getting under is about how fast you can stop this production of force to propel yourself back under the bar.
A good example is a Powerlifter who can produce a lot of force, but they don't have the elasticity to drop themselves under the bar. You can see this quite easily at the beginning stages of a Powerlifter that transitions to Weightlifting.
Increased Coordination
Jumps, throws and all of their variations take quite a bit of motor coordination. That is, your nervous system's ability to synchronously recruit all the appropriate motor units needed to perform a specific task. The more complex the task, like jumping, throwing, and sprinting, the harder that is to do. Which is why it's probably a bit easier to develop a very strong squatter, but much harder to take an average joe and make them a decent sprinter. The motor coordination involved in sprinting happens at a much higher rate, and is therefore likely harder to develop.
Anyways, Olympic lifting is another task that is fairly complex and takes quite a bit of coordination to complete both lifts. Just watch anyone who tries to snatch for the first time. If someone already has decent coordination or general athletic ability, they tend to catch on to the Olympic lifts quite a bit quicker than someone with no athletic background.
If we incorporate some plyometrics in an athlete's program this should develop some decent overall motor coordination, which should transfer to the main Olympic lifts. These can be a great added benefit to someone new to the sport that doesn't have a previous athletic background.
At the end of the day, nothing is going to get you better at Olympic lifting more than practicing the Olympic lifts very consistently. However, adding plyometrics for 10-15 minutes at the beginning of one's training sessions can give them some great added benefits complementary to the Olympic lifts.