Hosting Eurovision according to this article is worth somewhere from $100 to 600 million, which for a country of Azerbaijan's size is a fair amount. To make a quick comparison, the GDP of the United States is 316 times greater than Azerbaijan (used to be 2500 times greater, mind you), so an extra $400 million or so is like an extra $125 billion for the US. More important than that though is the opportunity to have the name Azerbaijan actually mean something besides the current "not sure if a real country name......" impression it gives to most now.
Nagorno-Karabakh: will Eurovision 2012 have an effect on this? Hopefully it will have a positive one. The war there in 1994 and the subsequent de facto but not de jure ownership of the region by Armenia is why those Armenian and Azerbaijani media sites one finds online all seem to be devoted to trashing the other side. "Why is Armenia/Azerbaijan so belligerent?" "Armenia/Azerbaijan makes real offer for peace that Armenia/Azerbaijan just ignores, like always!" "Armenian/Azerbaijani soldier shoots Armenian/Azerbaijani civilian!" etc. etc.
This war of words is not going to cool down over a year of course, but one would imagine that Azerbaijan would want to keep things as uncontroversial as possible over at least the next year, while the eyes of Europe are on it and people are beginning to acquire their first impressions of the country.
You can see the video of the team from Azerbaijan (Ell and Nikki) as they win in this video. Most definitely not my kind of music. I am glad to see Azerbaijan win though. It would be even more interesting to see Armenia or Georgia win the next round too.