Here is a good explanation said much better than I could.
Let's start by looking at a single metal unconnected to any other metal. It is made of atoms that have positively charged nucleuses (okay, "nuclei", Miss Crabapple) which are surrounded by electrons which balance the charges, and all is well. Then let's say these atoms become exposed to a corrosive media (an electron stealer). The corrosive media steals an electron. Now that atom is no longer an atom, but a positively charged ion in search of an electron; so it dissolves into the media in search of an electron to balance it. So, what actually causes corrosion is the loss of electrons from the metal.
Metals are electrically conductive, i.e., electrons can run through them from one spot to another just as they run through a wire. So if two different metals are mechanically connected in any fashion at all without an electrical insulator between them, electrons can run through them.
Now take a chunk of two different metals connected together and expose them to a corrosive media which is stealing electrons. The way galvanic protection/corrosion occurs is: when the nobler metal (the copper in this case) has an electron stolen from it by the corrosive solution, it has a greater affinity for electrons than the baser metal and immediately steals back an electron from the baser metal (aluminum in this case). The result is that the copper atom remains a balanced atom of metal, and the aluminum atom comes up short and corrodes into solution.