A media player is an application that plays media.
Typically, the media players are "integrated solutions" for playing files. Often, you just launch the application, try to play stuff with it, and it plays it - no matter what format the file is in.
There's only one problem with these: Before this fad, each "media player" specialized in playing one medium. You know: To play .avis, you wanted to launch Windows Media Player, to play .movs, you wanted QuickTime Player, for .ra you wanted RealPlayer and for .mp3s, you wanted Winamp. Then someone noticed that Winamp is a Really Popular Program, and that it plays a lot of different formats - my god, to get riches, make your media player play them all!
The result? If you want to install a new media player to Windows, expect it to associate itself with every file format known to man. Luckily, some programs behave nice and ask which formats you want to play with it; I can install Winamp, and then install WMP, and expect the .avis to play with WMP and .mp3s with Winamp. Then, there are greedy bastards of programs like RealPlayer, but that's another issue...
Now, everyone and their dog is making "media players"... the market is flooded with these things. Take your pick.
Windows' file association remains one of the problems. This is probably Windows' fault: One file type, one default application. In other OSes, the division is often easier.
Some popular media players for different platforms: