Bellhousing (aka bell-housing or bell) is a colloquial term for the component that aligns and connects the transmission of a vehicle to its engine, and which covers and protects the flywheel/clutch or flexplate/torque converter.
[1] It derives its name from the bell-like shape that those internal components necessitate.
The starter motor may mount to it, and it may support clutch and/or shifter linkage.
[2] A Bellhousing may be a separate housing bolted to the gearbox, or it may be an integral portion of the transmission housing, particularly with front wheel drive transmissions.
An integral bell has a front bolt pattern that matches the engine to which it will be paired, and a divorced bell additionally has a rear bolt pattern that matches the gearbox to which it will be paired.