Fast Lenses Have a Wide Aperture
Although the aperture of a lens refers to the size of the hole in which the light passes through the lens to the film or image sensor, lenses are ranked in speed. For instance, a lens with a very wide aperture (like f/1.2 or f/1.8) is a fast lens because it lets in more light, allowing you to use a faster shutter speed while maintaining exposure. A lens with a very small aperture (like f/5.6 or f/11) is a slow lens because it lets in less light, requiring a slower shutter speed to maintain exposure.
Aperture (F-stop) is a major component in determining depth of field (DOF). Fast lenses allow for shallower depth of field. This effect, of a very shallow field of focus, creates a trademark cinematic look for videographers because it allows subjects to be separated from the background. This effect, in combination with light sensitivity, makes fast lenses preferable to slow lenses for videographers and photographers alike.
A "Prime" Lens Usually Means a Fixed Focal Fength
A fixed focal length (FFL) lens is simply a lens that does not zoom. Its focal length is fixed. This is obviously different from a zoom lens, which allows the user to change the focal length using movable lens parts within the lens body. Zoom lenses are ideal for users who need variable focal lengths available to them without changing lenses. Video lenses tend to be zoom lenses as zooming whilst filming is an essential feature for many videographers and filmmakers.
Prime Actually Means Primary or Chief Lens
When people refer to a prime lens, they’re most likely referring to a fixed focal length lens. Historically, however, prime simply means primary or chief lens; the primary lens in a combination lens system. A prime lens could be a fast lens or it could be a slow lens. A prime lens can also be a zoom lens. Primary zoom lenses are usually referred to as variable prime lenses. Since FFL lenses generally have better optical quality than zoom lenses, FFL lenses make better primes.
Fixed Focal Length Lenses are Typically Fast Lenses
Since FFL lenses don’t have the additional glass or mechanics required to change focal length, there’s less obstruction to the light. Additionally, FFL lenses are generally shorter (wider) then zoom lenses, which tend be longer (more telephoto). Hence, FFL lenses are generally faster than zooms. Of course, these are generalizations, not rules. There are wide, fast zooms and slow FFL lenses. But generally, since most prime lenses are fast, fixed focal length lenses, you’ll see all these terms used interchangeably.