AVI is a container; just like MOV or MP4, it can contain many different things inside.
Quicktime Player CAN play AVI files, but of course not all of them.
(Examples: AVI files with H264 video, or PhotoJPEG video DO open and play in QT Player)
The problem is that there are many CODECs - some of them are very old, or not widespread - and Quicktime Player supports only a small number of them.
VLC, on the other hand is the Swiss Army Knife of video playing, it can play just about anything; but it is not very good for converting stuff.
MPEG Streamclip, even though it is now a few years old, is a very useful tool if you need to convert. In addition to supporting many legacy codecs (it is based in the old Quicktime frameworks, so it can play anything that old Quicktime 7 can), it can convert to many formats AND different containers - you can convert to, say, h264 in MOV, MP4 or AVI containers, for example (though by now I can't think of a reason anyone would want to create AVI files anymore).