In the aeronautical sense of the word, it is indeed the angle between two planes (no pun intended) at their axis of intersection. Now imagine that these planes are actually wings. The most pronounced examples I can think of are low-wing light aircraft like the Beechcraft Bonanza, where this design is most apparent.
So why do they do this? Imagine an aeroplane with significant dihedral flying along in... uh... Micronesia. Since we've all been through junior high physical science, we know how and where the wing produces lift, and based on this, the lift of either wing is angled inward because of the dihedral. Let's say we roll to either side a bit. The wing that raises up is going to produce less upward lift than the wing that lowers down, which now produces lift that isn't quite as angled into the fuselage in relation to the axis perpendicular to the axis of intersection.
I'm making this sound more complicated than it needs to be. The basic idea is that when one wing drops and the other rises, the aeroplane will automatically try to make itself level.