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Imagine you're inside a big cardboard box, and you're trying to read a book. That's pretty hard to do in the dark, right?
Okay, so let's poke a pinhole in the box. Not much better, is it?
But what if you cut a hole that's 4" in diameter? You'd get a lot more light inside your box, wouldn't you? And that, of course, would allow you to read your book.
Well, that's what the lens speed is all about: the largest amount of light the lens will let into your camera (measured by the lens's "maximum aperture"). The wider the lens opens, the more light it allows into the camera.
The maximum aperture of a lens is expressed as an "f-number." The smaller the f-number, the more light the lens can let into the camera. (I'm skipping most of the technical stuff here.) So, for example, an f-2.8 lens can allow more light in than an f-3.5 lens.
And here's where it becomes important: A faster lens can shoot a low light scene at a lower ISO rating than a slower lens. And that means you'll see less noise and less "grain" in the resulting picture. All other things being equal, a faster lens will always yield better pictures in lower light.