Red velvet cake is a moist cake that has a deep red color. The flavor comes from a blend of cocoa, vanilla, and a bit more butter than you put into most cakes.
The result is less rich than pure chocolate or even devil's food cake, but much more flavorful than white or yellow cake. I consider cream cheese the definitive red velvet cake icing, but pretty much any white icing is traditional. Some people prefer vanilla or buttercream.
The red color in most modern cakes comes from red food coloring, though some recipes use weird stuff like beet juice. In old cakes, it came from the cocoa powder-- cheap methods of making cocoa powder back in the 1800s tended to turn the cocoa powder red, which turned the cake red.
Making a good red velvet cake from scratch can be challenging since you won't get the dramatic red color without ruining the cake if you use too much cocoa (and too little makes it bland).
If you want to try red velvet cake sometime, a good local bakery may have it. There's also some entirely acceptable box mixes for it at supermarkets.
Be wary of red velvet cakes from supermarket bakeries, though-- sometimes you'll just get devil's food cake with so much red dye pumped into it that it takes on this nasty, bitter chemical taste.