In the books, Stannis gets to this point where the good and bad angels on his shoulders, Davos and Melisandre, both confront him, with Melisandre encouraging war on the south and sacrificing Edric Storm, and Davos saving the boy. Then as Stannis is about to punish him for it, Davos reveals the letter, and we later find out that Stannis made the decision to come north, independent of Melisandre (and probably against her wishes). It's very important as it's the moment where he stops being selfish and starts acting like a true king should, leading himself rather than being led by Mel.
In the show he ignores Davos letter and is going to go through with executing him until Mel says actually he shouldn't and they should head north, so Stannis does as she says like a little bitch. He doesn't change as a character at all, and comes across as far more selfish and unkingly.
The book quote posted above sums up what Stannis character arc from books 2 and 3 is supposed to be, and the show completely turned it around, and replaced it with nothing. If they'd at least given him a different arc and development then I could cope with it, it's the fact that he's just her bitch that boils my blood.
And now I'm ranting. Fuck I hate that scene.