A Flamewar is when a particular thread and the people posting to it descend into an extended bout of arguing over generally meaningless points usually involving a lot of insults and bringing each others skills, education, lineage, ect into question. usually in the most unpleasent manner possible.
So basically an online shouting match...
You can find a longer definition here:
http://en.wikipedia.org/wiki/Flaming
Hope this helps