Bonus feats allow a player character to choose a feat in addition to the feats obtained from the usual level progression. Aside from the human bonus feat, these are obtained at certain class levels, as set forth in each class' description, and are selected from a restricted list of feats, also set forth in each class' description. Sometimes the term is also used for feats obtained without a choice being made, in which case more racial feats can be included.
An epic bonus feat is a bonus feat choice obtained because of an epic class level. These are significant in that few classes receive any pre-determined class feats at epic levels, while all epic classes gain a choice of bonus feats at regular levels. (This is the reverse of pre-epic levels, when few classes receive a choice of bonus feats, but most do receive pre-determined class feats.) However, in terms of game mechanics, these behave no differently than other bonus feats that allow a choice; each class has a single list of bonus feat choices that is used regardless of whether or not the bonus can be called "epic". Some choices might only appear as epic bonus feats, but this is a consequence of those feats' particular prerequisites being impossible to meet otherwise, not something intrinsic to a bonus being granted by an epic, rather than pre-epic, class level.
The single list of choices per class has an interesting consequence that may be unexpected to many (and that is probably unintended, yet accepted, by BioWare). Every time a class-granted feat allows a choice, that choice is made from the class' list. This includes such things as choosing a race for a favored enemy. Before Hordes of the Underdark was released, this was inconsequential, as, for example, the list of choices for rangers included only favored enemies. With the addition of epic bonus feats, the class lists were expanded, making more options available, particularly once a character becomes epic (hence meeting the prerequisites of more choices on the list). For example, an epic character taking a fifth ranger level could potentially substitute epic prowess (a ranger epic bonus feat) for the favored enemy normally obtained at that level.