Every participating country sends an artist who will perform singing their song and in the end people at home can vote (except for the contestant from your own country) for the song they like most. I say song, but the performance plays a part in this too, so the artists often go all out, resulting in some pretty weird acts (like Windows95man linked above). During the finals, there are jury votes too and they can give a few votes, each of which has a number of points up to 12 (the infamous douze points) - they basically create a top-10. The artist who gets the most points, wins and their country will host the Song Contest next year.
I haven't heard many really good songs in the first semifinal, but Italy's is good. But they didn't participate in this semifinal, they are automatically through to the finals because their song is that good.