How do solar panels supply energy for spacecraft?

Why do solar panels look like wings?

Solar panels are not wings, but they are shaped and positioned the way they are for reasons similar to the reasons wings are shaped as they are. The answer has to do with a need for large expanses of surface area that are balanced on either side of the craft.

Solar panels need to have a lot of surface area that can be pointed towards the Sun as the spacecraft moves. More exposed surface area means more electricity can be converted from light energy from the Sun. It is also not in DS1's interest to have one solar panel positioned so that it casts a shadow on the other one. Because of those reasons, the solar panels are flat sheets to either side of the spacecraft.

Wings also need to have large expanses of surface area and not interfere with each other, but for different reasons. In the case of an airplane,  the wings are shaped so that when the plane moves through air, they give the plane lift. Airplane wings have to be level with each other or the plane will not fly straight.

Why do solar arrays need to be oriented towards the Sun?
How do solar panels convert the Sun's energy into electricity?
How do solar concentrators work?

Why do solar panels become less useful the farther they get from the Sun?
What components are where on DS1?

How much power does DS1 use? How much power does it produce?