Well... if you are training for power, they are very useful. Beyond that, it's just a class the fitness clubs promote to make things hard for the people who take them. But seriously, if they were really doing plymetrics, they wouldn't be able to walk or do other activities for a day or two. They are meant to be very strenuous, short bursts of very high intensity, anaerobic efforts. Done incorrectly, they end up doing more harm than good. Done correctly, it can improve power by training you to use the highest amount of force in the least amount of time.
The idea of strength lies in the fact that during movement, as a muscle lengthens (stretches), it produces a sort of stored energy. Then as the muscle contracts and shortens, the stored energy can be used to increase the force of the contraction. Plyometrics allows you to take advantage of the stored energy so that you can basically take more of that stored energy and use it during the contraction of the muscle. This is how power is increased.
The correct use for plyometrics is to build up the weights over time- weeks and months. Once you've built up strength in the muscles, you can procced to plyometrics. This is NOT a long term exercise done over months, as the efforts are too strenuous to maintain. Also, building the maximum amount of strength you possibly can is critical to avoid injury and to ensure you are getting the maximum results you need from doing the plyometrics. So... you start first by increasing your weights over time (weeks and months), then you move to plyometrics. Then when you do move to the cycling (I assume you have a training program that complements your strength training so as you come off your plyometrics, you are ready to increase your cardiovascular demands), when the time comes for you to do power drills, you will have trained your legs for those short bursts of high intensity effort required for the drills.
If you're training for endurance cycling, there isn't much need for power training. They're more for the shorter efforts like track racing or criteriums.... but that's not to say there's absolutely NO need- some coaches say there's no need. I say maybe about 5% of your total training time needs to focus on plyometrics and power training if you're just training endurance. It varies with coaches, so talk with your coach before you decide what will work for you.