As a sports scientist I thought I would throw my 2 cents in.
To answer the original question, plyometrics will improve cycling performance. The question is, is it the best way of improving cycling performance, the most likely answer is no. There are better ways to spend your time training for cycling than doing plyometrics. Plyometrics are not cycling specific enough but can play a supportive role.
As has already been mentioned plyometrics is a very intensive form of training that has a very high injury risk. It really should only be the domain of the highly trained althlete and / or done under the supervision of an expert.
The pros of plyometric training is that you need very little equipment and you can train almost anywhere. Its a very functional exercise. This means it translates very well into normal human movements and needs. However cycling is the exception. Cycling is an unnatural movement for humans. We do it rather well but nothing in our development over the centuries has required a rotation action from our legs. As such the functional translation of plyometrics to cycling is almost non existent. What plyo does do is train 2 very important aspects of muscle contraction.
1. It trains muscle balance. Plyo demands functional co contraction form all muscles involved in a movement. We are not just focusing on quads or hamis as you may with weight training. The result is more muscularly balanced movements which can increase power through efficiency and reduce the risk of injury in normal activities.
2. The second factor is the muscle stretch shortening cycle or SSC. This is a theory that muscles, tendons and ligaments store potential energy when strectched that assists a subsequent contraction. For example, pushing down on a pedal needs the quads to contract and the hamis to lengthen. Potential energy is stored in the hamis as they are stretched by the quads. This energy can be released on the pedal upstroke which assists the hamstring contraction and gives a more powerful contraction. The same is true for the subsequent downstroke with the quads now releasing their potential energy store during the supstroke. Shew! Make any sense. Plyo is one way of optimising this effect. It also works on the neurological component as Hammie mentioned. But the explanation of this is 5 page post in itself.
The cons of plyo is the high risk of injury, the severe muscle stiffness over the following 72 hrs (DOMS) and the lack of specificity. But I do include them as part of the cross training programme of the athletes I manage.
Plyometrics would suit rugby, soccer, hockey players more than cyclists.
Better stop their as I am sure most of you are bored to tears by now.