What is iPhone Baseband?

The general definition for baseband can be found on Wikipedia.
The ‘baseband’ is the generic nickname given to the internal components of the iPhone that handle the phone calls and Internet access. This ‘baseband’ is a tiny and unique independent computer system that runs inside your iPhone, it is separate to the main system that handles the applications (such as email and google maps) and it talks to the main part of the phone over an internal communications network.

Think of it like a cable modem or other peripheral that is attached to your home PC that needs occasional updates. When a software update is released and presented to you within iTunes the baseband is sometimes updated (to fix bugs or add new features).