When I first started baking, I thought white cake and yellow cake were the same thing - and even today, I'll use yellow cake in place of white cake because they're kind of interchangeable.
But it's come to my attention that a lot of people don't know the difference. So, I've decided to break it down for you:
Yellow cake gets its trademark "yellow" color from the amount of egg yolks in the batter. My yellow cake has 4 whole eggs in one small cake, which makes for a lot of yolks, though the batter turns out surprisingly light. It still has an obviously yellow tint. The yellow ingredients in cake - eggs and butter - will also make your cake more dense and moist.
A typical white cake will have almost twice as much egg white and no egg yolk at all. This makes the batter much lighter in color (thus the "white" name) and when the whites are beaten, can make the cake lighter and more airy.
Personally, I prefer the dense cake and rich flavor that egg yolks bring to the table, but if you're in the mood for something a little lighter, white is always a good option. ;)