to compel (somebody) by force or circumstance
(usu in passive) to put (somebody) in one's debt by a favour or service
We're much obliged to you for all your help
to do a favour for (somebody)
She obliged the assembled company with a song
to do something as a favour; to be of service
He's always ready to oblige
[Middle English obligen via Old French from Latin obligare to bind to, from ob- + ligare to tie]