to make someone morally or legally bound to do something or take a particular course of action, to compel them and hold them responsible;
e.g. This contract will oblige you to have no interactions with our competitors.
(verb)
to do something as a favor to someone, especially in order to please or help them;
e.g. I will oblige him for his generosity by doing these tasks for him.
(verb)
to be grateful or indebted to someone due to a service or favor they performed, or to make someone grateful or indebted by doing them a favor or service (often used as "be obliged");
e.g. It would oblige me if she is willing to give me a ride.