A Popover is a quick bread that has a high proportion of liquid, which creates steam that helps leaven the bread. They 'pop over' the sides of the muffin tins. (The basic recipe is flour, eggs and milk).
The 'invention' of popovers, like many food dishes, most likely took place by accident when someone used too much liquid in a recipe. The recipe for popovers is very similar to that for Yorkshire pudding.
(Yorkshire pudding dates back to at least 1796, with a recipe in the 'Art of Cookery' by Hannah Glasse).
The earliest recipe I know of for popovers is in the first edition of the 'Boston Cooking School Cook Book' by Mrs. D. A. Lincoln (1884). (This was before Fanny Farmer became director of the school in 1891).
Although Webster's Dictionary sites a reference for 1876, they do not specify the source.