do you have any codec packs installed?
avi files are a container that can contain many different types of audio/video, and to play back a file you need to have the decoders for both the audio and video files inside it. In many cases the audio will use something common that all computers have the decoders for however windows doesn't come with many decent decoders for video (it only comes with ones that make huge files). So for the vast majority of videos you will need to install the decoders for the video file.
Thankfully there aren't that many different codecs that get used for encoding video, just a handful of decent ones get used - so quite a few people have made codec packs, these are installers with several of the most common codecs in that can be used to play just about any file you download.
There are several common codec packs you can use, you only really need one though as they normally just contain pretty much the same thing
Several common codec packs:Codec pack all in oneKLite Codec PackXP Codec Pack
(just pick one of them, any should do for most videos)