What's the difference between a "fast lens" and a "slow lens"?

Kinor Lens
Kinor Lens

A lens is often referred to as "slow" or "fast", because of its aperture. The "faster" a lens is, the more the aperture is allowed to open (the wider an aperture) AND the lower the number it can go in f-stops. Faster lenses let more light in to hit the focal plane and allow a faster shutter speed. So a cinema lens that can be set to f1.4 is considered very fast, while a cinema lens that can only go down to f2.5 is considered fairly "normal". A cinema lens that's lowest setting is f5.6 is often considered "slow".

Note that the wider a lens can open up its aperture (in f-stops), the shallower the Depth of Field ; which basically means that the faster a lens, the more selective focus it can offer. Sometimes fast lenses are called Super Speeds.