Velvet cakes originated in the Victorian Era. During the 1800's, luxury cake recipes would call for cocoa. The cake would have a smooth and soft texture due to cocoa's properties. A chemical reaction between the cocoa and acid gave the cake a red color. Natural cocoa is acidic and reacts with baking soda and buttermilk.
Around 1943, "The Joy of Cooking", a popular cookbook, presented the first red velvet cake. Durign WWII, people had to ration off food and supplies. Sugar and butter were part of the rations, so some bakers used beet juice in their cakes. The beets made the cakes pretty (and red!) and soft.
There are a lot of different theories as to who invented the red velvet cake and who deserves credit for bringing it to the United States.