Random fills in PCB in Eagle
A dimension error means something is too close to something else. In this case it looks like your silkscreen is too close to your hole (shown by the rectangular outline). You can either cut back the silkscreen, ignore the error (most fab houses won't lay silkscreen over holes anyway, they'll cut it back themselves), or move the component (if the hole is not part of it). 

EDIT: I take that back, it is not the silkscreen layer. OlinLanthrop is correct in that it is not the silkscreen, but he is not correct in which layer is the issue. I should have looked a bit more carefully. The error box shows what layer the error is on -- #1, which is the top layer. This suggests that the red trace (on the top layer) is too close to the hole--Not the bottom layer (blue) or the silkscreen. Notice the hashed area is also red, meaning the conflict is with the "red" (or top) layer, if I remember correctly.

I expect if you neck the trace down a bit, or adjust your rules to meet your fab house's abilities, your error will go away (if the trace is not in violation of the manufacturer's rules).