In this context, it means "that's all right" and is assuring the person who said "thank you" that whatever the reason (or cause) he said thank you for, is "all right" or acceptable in the particular context of the two people.

A: "Thanks very much" is just like saying, "thank you," but with a little more gratitude as it is "very much" B: "That's OK" means that it is fine or alright

It probably means that the person who says, "It's OK," wants the other person to know that it was not an inconvenience for him to do the kind thing that he is being thanked for. You could also say, "Don't mention it."

It means it's all right

Thanks very much