F-stop determines depth of field (very simply speaking, as my camera experience is maybe 1 level above yours). The lower the F-stop available, the more flexibility you have in taking shots in lower light (for one thing). I'm sure the real photographers will chime in shortly.

18-200 seems like an awfully wide range for a zoom lens--going from wide angle to telephoto seems odd to me. How much does that thing weigh?

I am the Doctor, and THIS... is my SPOON!