To oblige is to do something you have to, because you're bound by either good manners or the law.
You are obliged to pay back your student loans, or for your portion of the dinner bill. You may also feel obliged to bring a gift if you're invited to a wedding. You can also tip your cowboy hat and be "much obliged" if someone does you a favor. The French phrase, noblesse oblige means basically that "privilege entails responsibility," or that the wealthy are obliged to do something productive in the world and not just sit around polishing their silver spoons.