Maximum power is the ability to apply your strength at speed, which is more important, in many sports, than maximum force.
For example, an elite sprinter's foot will be in contact with the ground for only about 100 milliseconds, presenting finite window in which to apply force. It's physiologically impossible to achieve absolute maximum force in less than 400 milliseconds, so the term maximum power refers to the ability to quickly produce and apply force, despite being some way short of any absolute maximum.
Achieving maximum power is important in every sport. In track and field, jumps, throws, sprints require the ability to produce power very quickly at one, or multiple, moments in time. For specific events like gymnastics or waterskiing, athletes need to be able to apply power to jump or vault at specific times.
Improving maximum power is a two-step process:
First of all, athletes have to be strong, so the more muscle they have and the greater maximum strength they have, the more power they can produce. But, given that once you've got that, then you need to train for peak power and use exercises and loads that develop peak power more specifically
Secondly, normally exercises which involve moving a load as quickly as possible, are used to enhance maximum power. The principles of training are the same across all sports, but it may be necessary to choose different exercises for different sports.