A motherboard is the complete printed circuit board (PCB) that holds all the other components. The CPU and any expansion cards plug into it, and it has the connections for ports such as USB and PS/2. If you look inside a desktop computer, it's about one square foot in size and should be the largest PCB in there.
All components of the computer are connected to the motherboard, either by
- being directly integrated into the PCB assembly,
- plugging physically into a slot or socket mounted on the PCB, or
- plugging into a cable connector or header pins mounted on the PCB.
The chipset usually refers to a particular set of components which are directly integrated to the motherboard. For specific details you should briefly read the Wikipedia article on chipsets, but usually the chipset consists of two chips, known as the northbridge and the southbridge. The northbridge is generally responsible for core system interconnects (memory, CPU) while the southbridge manages connections between other components such as PCI cards and USB devices.
In a more generic sense, chipset can also refer to a specific device controller chip that is (normally) connected to the PCI bus (ie the southbridge), depending on the context. For example, the SATA controller chip is sometimes referred to as the SATA chipset, whether it's integrated into the motherboard or on an add-on PCI(e) card. In the same way, one can talk about a RAID chipset or USB chipset or network chipset.