Over Easy - Eggs cooked "over easy" means that it gets fried on both sides, but the yolk stays runny. To make one, you cook the raw egg just until the whites are set on the bottom, then you quickly flip it over to cook the other side. "Over" refers to flipping the egg, and "easy" refers to the doneness of the yolk. You can also cook eggs "over medium" and "over hard," depending on how cooked you prefer the yolk!
Sunny Side Up - This means that the egg is fried just on one side. The yolk is still completely liquid and the whites on the surface are barely set. You can cover the pan briefly to make sure the whites are cooked or baste them with butter. We've always assumed that the name refers to the way this egg looks like the morning sun.
How do you like your eggs?
Related: Top Five: Ways to Eat a Fried Egg