.rar is an archive format, like .zip. You can download any number of extraction programs to open it up. Personally, I use WinRAR, but there are other alternatives out there.
.flac is a lossless format for audio. It doesn't play on many (any?) MP3 players, although Winamp has a plugin you can play it on your computer with. You can also convert the FLACs to .wav files, which are playable on pretty much any device out there, and can be burned to an audio CD. FLAC is the preferred file type in this and virtually every other trading community for sharing purposes.
.mp3 files are lossy audio. Basically, in order to make them considerably smaller than FLAC/WAV files, data is removed from them. This means sound quality is removed. It takes a trained ear to hear the difference between a FLAC and a high-quality MP3 (320kbps), but the difference becomes appreciable quickly if you listen through high-quality headphones, or just have an ear for it. While it's perfectly fine to convert FLACs to MP3s for personal use, it's bad form to share or trade MP3 files or MP3-sourced files. The reason being that once the data is lost, it's gone forever--i.e., changing an MP3 back to a FLAC does not restore the data--so listeners should have the best file quality possible, and then be able to lossy it up themselves if they so choose.
"Do you think I should keep this mustache? Did you say no? F--- off."