When you load a file and the cue sheet into foobar, there is an verify option, and when I clicked it said the status was "ok". So does this verify that the file now is the same as when the cue sheet was made? What information of an audio file does the cue sheet contain anyways?

I do not know of this verify option you speak of, and I exclusively use FB2K for damned near everything. EDIT: Can someone explain to me this verify option, I have never used it.

The CUE sheet contains all track information and time position when you rip a CD. It is used for either image files to point to the track points, or it dictates the pregap of a track when ripping to individual files. CUE sheets are quite handy, I wouldn't recommend throwing them away.

Well, cuesheets do not contain all track info. Refer to this wiki article.
I've never seen the verify option for the cuesheets in foobar. Maybe it's something with the embedded cuesheets, but I've never used them. foosion can certainly help here