What he said. The wider the aperture (smaller the f/ of the lens), the FASTER the shutter speed you would be able to use and the FASTER (in general) it will focus, etc.
For dimly lit areas (wedding dance floor, streetlights) trying to focus with AF or even manual with anything slower (larger f/ numbers) than f/2.8 is asking for frustration...or at least extreme patience. By contrast, settings too dark to achieve accurate focus for an f/2.8 lens would be a piece of cake for an f/1.4 lens... and so on.
All things are a trade off. The faster the lens, the wider the aperture (which means the wider diameter the lens which means heavier glass which means more money). Manufacturers usually put their best technology and efforts into their fastest lenses at any given focal length. Insert additional dollars. Prime lenses (single focal length, "zoom" in by walking forward, "zoom" out by walking backwards) are generally faster than zoom lenses that cover that focal length. The primes in general are lighter and sharper as well. For comparable quality, they are also cheaper, but then you have but one focal length. In general, you have to get a pro quality zoom lens (usually an f/2.8) to be comparably sharp to the mid level prime glass...which would be faster. It all comes down to needs and preferences.
For chasing children, I prefer my 24-70 f/2.8 zoom lens. It is plenty fast, and I can rapidly change the focal length when needed. When shooting still subjects (or those that follow direction), I greatly prefer primes for their sharpness and wider apertures. The other benefit of wider aperture lenses is their ability to blur the background by shooting at or close to wide open. That can help isolate a subject in a way that otherwise could not be done.
Depending on where you live, hit a local camera shop and rent one or two types and see what you like/need. Be sure to shoot them in challenging conditions (low light) before deciding. If no one rents near you, consider www.lensprotogo.com. I have used them, and their rates and staff are great.
Jim