When you forbear, you hold yourself back from doing something. If you're mad at your best friend, you might forbear to return her text messages for a while.
If you forbear to giggle during your teacher's stern lecture, that's a good thing. You keep yourself from laughing out loud, even though that's instinctively what you want to do. The Old English root, forberan, means "control one's feelings, or tolerate." A less common way to use forbear is as a noun meaning "ancestor." So if you're refraining from reading about your ancestors, you can say you forbear to learn about your forbears.