A popover is a GUI element visually similar to a popup, except a popover is part of the page from which it is drawn, even though it might obscure part of it.
A popover is a dependent GUI window graphically overlaying some, or all of, a window.
A popup is generally an independent window. A tooltip has more in common with a popover, but they are generally regarded as a popup historically.
An example showing a popover responding to user input: Example popover http://ui-patterns.com/image/1539/0/0/470