If you are obliged by a rule or law you are metaphorically bound by it—that is, you are required to obey it. The idea of binding links the word to its Latin source, ligāre, meaning “to fasten, bind.” In the most common modern uses of oblige, though, the idea of binding is somewhat masked: it is applied when someone is bound by a debt for some favor or service, as in “We’re much obliged to you for the help,” but in the phrase “happy to oblige” it simply expresses a willingness to do someone a favor, as in “They needed a ride and we were happy to oblige.”