Well, the key difference between FLAC and MP3 is that FLAC is lossless - no data is actually removed, as in MP3 compression. I keep all my CD rips in FLAC so that, should something happen to the CD, I'll have a near-perfect copy to replace it, rather than MP3, where each generation will degrade the music a little bit. The only problem is that now I keep 2 copies of my collection, one in FLAC and one in 192kbps MP3, to put on my MP3 player. But again, with storage being so cheap, it's not a bad deal.
I can't speak for OGG, though - I think I gave up after a technical pedant tried to explain the whole separation of OGG and Vorbis.
Plus, I like that FLAC is all free and open-sourced, so I can screw around with it if I want. From what I understand Windows Media 10 has a lossless codec that might actually give slightly higher compression, but I skipped it basically just because it's MS closed-product.
That's pretty much the difference - lossless vs. lossy. There are certainly smaller battles within the lossy world as to whose codec is the best-sounding or highest-compression, but I don't really worry about that too much.