I can see that confusion reigns in .avi questions as usual, so let's see if we can clear it up a bit.
.avi is what is called a media container. A container can include an audio track and/or a video track and often other things as well, such as subtitles. Other containers are .mov, .asf and the .VOB files found on DVDs.
There are many many audio and video codecs out there. You can see which is used in your movie by opening it in Quicktime and doing Get Info, but I think that formats that it can't recognize aren't shown.
To show a movie, the program you're using must support the container format, the video format and the audio format. Quicktime supports .avi, and has for a very long time (although it has gotten less picky with the format being absolutely correct with newer versions). What it doesn't support is every imaginable video codec out there. Fortunately, Quicktime supports plug-in codecs.
If you have a video that won't show, you start by updating Quicktime and then adding codecs. The DivX player above is one good addition, as is Flip4Mac. Other good ones are Xvid, MSMPEG4v1 and v2, AC3, and Ogg. Try googling for them, and come back if you can't find them.