From Mac Guides
The term "logic board" is generally interchangeable with the term "motherboard", the name by which it is more commonly known in the PC world. Apple refers to the motherboard of a Mac as the logic board. The logic board contains most of the discrete logic ICs, hence the name.
Over the last few years, Apple users have experienced persistent problems with the logic boards on some iBooks. Apple instituted extended logic board replacement past the normal warranty period for many of these iBooks.