It means to look at, but it sometimes has the connotation of looking at something to make an estimate instead of counting of measuring. For example, I don't know how much mayonnaise I use in the chicken salad. I just eyeball it. This means I estimate the correct amount by looking at it instead of measuring. If I'm dividing something into two approximately equal piles, I'll eyeball it instead of counting it precisely.

*verb *eyeball It means to look at :) He eyeballed her. I don't know if it's standard English though. I've never used it before and it's not a common thing. I'd say it's more colloquial. More like slang than proper English :)