The Eurovision Song Contest is not, despite the name, limited to Europe. It also includes Turkey and Israel. Details of its history can be found here.
Essentially, it's a kitschfest. In the UK it's a standing joke, and regarded with affectionate enthusiasm by students and various others. The quality of the music is...well, it varies, but generally speaking we're talking cheesy, camp, kitsch and mockable. Some countries take it pretty seriously - especially the former Eastern Blok countries, for whom any inclusion in a Europe-wide event is a big deal. It does kind of warm the cockles of one's heart, in a way, and yet it's also pretty hilarious. It's not like the Miss World contest, and yet I can't think of any other cheesy kitsch thing to take as a point of reference. Hmm.
As I understand it, there are two stages to the competition; the first stage involves shedloads of countries, and then they whittle it down to the 26 or so we get to see in the televised competition. In years gone by the judging was done by a handful of people in each country (heaven only knows upon what basis they were selected) and traditionally voting has been very political - eg Cyprus gives its largest vote to Greece, Norway gives big votes to Sweden and Iceland, France gives big votes to Belgium etc etc. Because of technological advances, however, we've now got phone votes and so the people of each country get to vote for who they like best. There's still an element of favouritism creeping into it, I think, but not so much as in years gone by.
It's tremendous fun. Camper than a row of pink tents, tasteless as a tasteless tasteless thing with no taste, and all made eminently more palatable by the reliable piss-taking commentary we get from the old stalwart of Eurovision coverage, the venerable Terry Wogan.