That gave me some problem for a while when I read about it as well.
Here's how I deicded to understand it. (Well, it works for me whether
it's the truth or not...)

Take it to an extreme--an airplane with a 90 degree dihedral. The
fuselage in in the "corner.
Now imagine one wing horizontal, the other wing vertical. All of the
lift component is on the horizontal wing, but the fuselage is at the
corner. The wing is pushing up, the fuselage is being pulled down by
gravity, and the plane rotates. The vertical wing is attempting to
push the airplane sideways. However, the fuselage isn't fixed in space
to rotate in just one place, so the sideways force actually does push
the airplane sideways rather than just rotating towards the horizontal
wing. Therefore, the fuselage "sinks", until it is in the low point
between the two wings (which would then be both pointing upwards at 45
degree angles.

Clear as mud? Oh well, I tried.