The basic difference between epic and mock-epic is that the former is supposed to be taken seriously, whereas the latter isn't. Mock-epic is a humorous take on the epic genre, parodying certain of its features for comic effect. For instance, Pope's "The Rape of the Lock" takes the most trivial incident imaginable—the theft of a lock of hair from an aristocratic lady—and makes a gigantic comic epic out of it, complete with battles, supernatural entities, and lengthy speeches, all elements taken from the epic genre.
But as these elements are put to comic use, we are not meant to take them seriously. Whereas we can only wince at the numerous brutal slayings carried out during the Trojan War in Homer's Iliad, we are meant to laugh at the “battle” that takes place in "The Rape of the Lock," which in actual fact is nothing more than a card game between aristocrats.
In essence, then, mock-epic involves the conscious exaggeration of the epic and its conventions for comic effect. The purpose behind this is usually to satirize the rich and privileged members of society in order to compare them unfavorably with their aristocratic forebears in ancient times, who, unlike their modern counterparts, don't waste their lives in the pursuit of trivial fancies.