These words have different meanings, and to add to the confusion, their spelling can be interchangeable. Here we will use the most common spelling for each one.
Forbear is a verb that means to “refrain, hold off, or hold back”—i.e. to not do something, to do something less, or to wait before doing something:
If you could forbear from chewing with your mouth open, we would be happier.
Note that the past tense of forbear is forbore, just as the past tense of bear is bore.
Forebear, on the other hand, is a noun meaning “ancestor.” And although forebear is correct, many people say forebearer, adding the -er ending for people. Either word is correct:
Our forebears / forebearers came to this country seeking freedom and success.
One good way to remember the difference between forbear and forebear is that forebear contains the fore from before, and it refers to people who came before us.