It's a name somebody thought up as 'Angel Food Cake' because it's so light and airy and it contains no fats like butter or margarine. First recipes appeared around the 1870s, apparently
There is a suggestion that angel cake - or 'angel food cake', as it is sometimes known - may have got its name as the opposite of a previously-existing cake called 'devil's food cake'. That, in turn, probably got its name because its chocolate content was seen as naughtily delicious!