iTunes: How to convert a song to a different file format - http://support.apple.com/kb/HT1550 - including information about different formats and discussion about compression.
Frankly though I think if it can't play mp3 then it cannot play AIFF. Do not confuse a file in AIFF format with the format that is used on an audio format CD which all players can play. I suspect that what you really need to do is burn audio format CDs. You can do this using your mp3 files.
iTunes 10 for Mac: Create your own audio CDs - http://support.apple.com/kb/PH1747
iTunes 10 for Mac: Disc burning overview - http://support.apple.com/kb/PH1746
The above confirmed by den.thed
Message was edited by: Limnos