In the original Macintosh model (as well as all the other B&W all-in-one Macs), the digital electronics (which are based on things called "logic gates") were on the "logic board", while the power supply and display electronics were on the "analog board". The terminology stuck.
So it comes from the fact that digital electronics rely on binary logic rules, mainly boolean math like AND, OR, XOR, NOT, etc.
tooki