logging means that every chat message you send or receive is saved to disk in some systematic way. just like email is saved in a big email structure, chat conversations can be saved for future reference.
just look for it to mention logging anywhere in preferences.
Logging is when the IM app records/logs everything you write/receive of text with your buddies to a text file (for later viewing, if you for example closed the window and forgot some important info that was sent to you...). There should be an option for turning this on or of in the prefs in iChat.