Don't Understand Lens Specifications

I am wanting to purchase a zoom lens. I see one which might be 24-120 mm f/3.5-5.6 Another might be 24-85 mm f/2.8-4.0 I understand the 24-120 and 24-85 zoom but I don't understand the significance of the f stop. What do I need to know to understand and make a more intelligent decision in the purchase of a zoom lens. Sorry for being so stupid. Thank you

The f stop listed in a lens spec is the widest aperture available for that lens. With a zoom lens, the widest aperture is different for the low and high ends of the zoom range so the f stop is listed as a range. In your example above, the 24-120 mm lens would have a max aperture of f/3.5 at 24 mm and a max aperture of 5.6 at 120 mm.
Since a larger aperture (lower f number) lets more light through the lens, a lens with a larger max aperture of f/2.8 would be preferable to a lens with a max aperture of f/3.5 if all other factors are comparable since it would allow faster shutter speeds in low light and a shallower depth of field if desired. In general, the larger aperture lenses carry a larger price tag as well.

Exactly - they're bigger and heavier too. Faster lenses come in handy in lower light levels and can give you the option of less depth of field. If either of these is important to you then faster lenses might make sense.

Nikon lenses, right? The current 24-120 also has VR and is the only one of that type in their lineup (currently) that has feature, so if you need it that's the one to get. Their 28-105 is really good too; there is another thread here about it.