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"
An old way of saying thank you; often associated with the Deep South and/or the Bible Belt, or the stinking rich
Jeeves: I've finished tarring the roof of the estate, sir.
Rich guy: Much obliged, Jeeves.
Jeeves: Thank you, sir.