Much obliged means that whatever was done is appreciated. Literally, it could be extended to mean that the person that says "Much obliged" now owes the other a favor. That the one that is obliged is under an obligation to pay back. Most people wouldn't expect a return favor though.
If a man is given a ride into town, when he gets out of the car, he might say "Much obliged". That would mean: "thank you for the ride. I am appreciative"
by Toastmaan January 12, 2009

Person 1: "I identify as Polygender"
Person 2: "Your parents must have been very abusive, I'm sorry"
Person 2: "Your parents must have been very abusive, I'm sorry"
by Toastmaan May 27, 2018
