What size freewheel do I need for BMX?

A typical BMX configuration is a 16T Freewheel (rear) and 44T Front sprocket. The lower the number of teeth on the freewheel equates to slower acceleration, more top speed. The higher the number of teeth equates to easier peddling with faster acceleration and less top speed.

Why do freewheels click?

That clicking sound is the pawls as they run across each ratchet tooth, sort of like a tiny Wheel of Fortune wheel. The pawls thread onto the hub body and spin whenever the bike is moving. The ratchet fits over the pawls.

What is the difference between a freewheel and a freehub?

The term "freewheel" refers to the whole gear cluster with the coasting mechanism inside. The freewheel is screwed onto a set of threads on the right-hand side of the wheel's hub. On a freehub system, the coasting mechanism is a sub-assembly of the wheel's hub.