The f-stop is a ratio based on the focal length and the actual size of the physical aperture (that is, the opening that lets the light in). For example, if you have a 50mm lens set to f/2, then the diameter of the actual aperture in the lens is 25mm (50/2).

It’s a bit counterintuitive at first, but remember that the smaller the f-number, the larger the opening. In your example, a 50mm lens at f/1.8 has an aperture of about 28mm, while at f/2.8, it has an aperture of about 18mm.

Those actual measurements, though, aren’t all that important. It’s more useful to think in terms of stops of light. Every “stop” represents a doubling (or halving) of the amount of light the lens lets in. For example, a lens at f/2 lets in twice as much light as a lens at f/2.8. And a lens at f/2.8 lets in twice as much light as a lens at f/4. You can see that it adds up quickly (the lens at f/2 is letting in four times as much light as the lens at f/4).

Looking at a chart like the one on this page can be useful as a guide for understanding stops.

Lenses with larger maximum apertures (that is, those with lower f-stops) are referred to as “faster” lenses, because the lower f-stop lets you use a faster shutter speed. As a practical matter, more light is good, but there are two important trade-offs. First, a faster aperture means a shallower depth of field (less of your scene in focus). If you’re trying to isolate your subject and blur the background, as you might with a portrait, for example, then a shallow depth of field is good. But if you want all of your scene in focus—say, for a landscape, or a street scene—then you need to stop down to a smaller aperture (that is, a larger f-number). Second, faster lenses are typically larger, heavier, and more expensive than their slower counterparts.

All that said, f/1.8 primes can often be the sweet spot for smaller affordable primes, and that’s a good place to start.

EDIT: By the way, if you’re just starting out, these videos are a great introduction to the exposure triangle, one side of which is the aperture.

EDIT 2: As to your question about events, a lot of event shooters use f/2.8 zooms, which combine a relatively fast aperture with the versatility of a zoom lens. I’m sure some use primes, too, although likely on a second (or third) camera. The f/2.8 zoom is the work horse.

Vague generalization, but 1.8s are often cheap plastic lenses. Whereas 2.8s are more often pro quality zooms.

The cheap plastic lenses can have awful aberration and muddy color and sharpness wide open, especially in low light, therefore to get the best quality out of your lens, you’ll probably be closer to 2.8 anyways.

1.4s, however, are much better lenses than 1.8s, and primes are generally better than zooms, but at the pro level it’s really hard to distinguish 2.8 primes vs 2.8 zoom.

With primes, I shoot around 1.8-2.2 often, and 1.4 in low light. 50 at 2.0 is probably my favorite look, but all primes look beautiful at 2.0.

Lastly, 1.4 to 2.8 is four times the amount of light transmission. That’s a big jump when you’re in the lowest light environments.