Competitive programming is a mind sport usually held over the Internet or a local network, involving participants trying to program according to provided specifications.
Maybe you've heard about olympiads like IBO, ICHO or IMO, well then IOI is the most prestigous olympiad for high school students in competitive programming.
Sounds interesting? Well, check out some well-known websites in CP (and the actual problems too):
First download a suitable editor for your enviroment:
Most contestants use C++ for coding, so go ahead and download compiler to run your program.
You can also find some useful links in this blog.