Not sure if this discussion is entirely allowed, but since it has non-pirate applications, I'll bite.
It basically entails modifying your Wii to allow you to install custom applications and games (homebrews). The Homebrew channel can be though of as the portal to all your homebrews, allowing you to install/run things like a media player, user-created games, USB emulation software, and installers. I've currently got my Wii set up as a media player (among other things), streaming videos from my PC to my TV over my WiFi network. You can also load media from a portable HDD or other storage medium.