The motherboard (mobo for short) is the main (and sometimes only) printed circuit board in a personal computer; as much functionality as possible is packed on this board, to save the cost of connectors to other boards.
It will also often contain connectors for a bus for optional cards to provide extra functionality. In early PC motherboards, this included cards to connect to local area networks, hold the hardware to drive the display, etc, but much of this has now been standardized on the motherboard.
There is sometimes provision for a daughter-card, if all the desired functionality cannot be fitted onto the main card; such cards may be optional, or mandatory.
Main memory is often contained on small cards that plug into connectors on the motherboard (e.g. SIMM memory modules); first to allow easy replacement if there is a failure, but mostly to allow the system to be upgraded with more/larger memory cards.