A fast lens is one with a wide maximum aperture, meaning a low minimum f-number such as f/1.4, f/1.8, or f/2.8. A slow lens has a narrow maximum aperture, perhaps f/4, f/5.6, or f/6.3. The terms describe how much light the lens can gather wide open, and photographers often call wide-aperture optics fast glass.
The names come from shutter speed. A lens that lets in more light allows a faster shutter speed at the same ISO and scene brightness, which is why it is called fast. In dim conditions a fast lens can mean the difference between a sharp frame at 1/250 second and a blurred one at 1/30, without resorting to high ISO and the noise that comes with it.
Beyond light gathering, a wide maximum aperture gives shallower depth of field and stronger bokeh for isolating subjects against soft backgrounds. Shooting wide open on a fast lens is the classic route to creamy portrait backgrounds and low-light atmosphere. A fast lens also feeds the autofocus system and viewfinder more light, which can improve focus speed and accuracy in the dark.
These benefits come at a price. Wide-aperture lenses need larger glass elements, so they are heavier, bulkier, and more expensive than their slower equivalents. The fastest options are usually prime lenses, since building a zoom that stays bright across its range is far harder and pricier. Many affordable zooms are variable aperture designs that grow slower as you zoom in, such as f/3.5 to 5.6, while a professional zoom that holds f/2.8 across its range is large and costly.
Speed is relative to focal length and format. An f/2.8 telephoto is considered fast because that aperture is hard to achieve at long focal lengths, while an f/2.8 wide-angle is ordinary. The classic affordable fast lens is the 50mm f/1.8 nifty fifty, while a 70-200mm f/2.8 is the workhorse fast zoom for events and sports. Video shooters describe the same lenses by their t-stop, which measures actual transmitted light rather than the geometric f-number.
When deciding whether to invest in fast glass, weigh how often you shoot in low light or want shallow depth of field against the real cost and weight you will carry. Remember too that most lenses are softest wide open and that the thin depth of field at f/1.4 is unforgiving of focus errors, so the widest aperture is a creative option rather than a setting to leave parked. For many photographers a single fast prime is the most transformative lens they own.
A useful way to shop is to decide what the widest aperture is actually for. If it is low-light shooting, even an f/1.8 prime transforms what you can capture, while if it is mainly background blur, a longer focal length at a moderate aperture can separate a subject just as well as a shorter, faster lens used up close.