You should be able to play H264 encoded video - so if your AVI file is H264 encoded you should be OK.
Search for omxplayer on the forum for using the player standalone, or XBMC or OpenELEC.
Principal Software Engineer at Raspberry Pi (Trading) Ltd.
Contrary to popular belief, humorous signatures are allowed. Here's an example...
“I think it’s wrong that only one company makes the game Monopoly.” – Steven Wright