Did you ever fly a Kite?

Remember how you would tie a string across the back to "Bow" the surface?

That's dihedral.

Without that bow, the kite would wobble for a bit, then turn sideways into the wind and fall. But because of the bow, if one side turns into the wind more than the other, it gets a more direct hit from the wind.

In the illustration below, you can see how the wind affects the surface of a Kite. Next you can see how this same priciple is applied to a wing.

And finally, you can see how dihedral will help an inverted wing right itself.