Emma is happy because now she doesn't have anything to conceal from Mr Knightley. Her problem is solved by Harriet marrying Mr Martin. If Harriet had stayed single things would have been awkward between her and Emma, and Mr Knightley would probably have noticed this - their awkwardness with each other, that Harriet would not spend as much time at Hartfield as she used to, etc. And since Emma could not betray Harriet's trust and tell Mr Knightley the reason for this, she would have to keep it a secret which she didn't like. So Harriet happily married to Mr Martin means that Emma does not need to hide anything from Mr Knightley because the problem no longer exist.