It's a distinctively British phrase that adds a friendly or light-hearted tone to a statement. They've jolly well made a good cup of tea.
Pro Tip 2/3
Assertive Nuance
Suggests the speaker is insisting on something; often used to reinforce one's point in a discussion. You jolly well know it was your turn to do the dishes!
Pro Tip 3/3
Contradictory Emphasis
Can stress the speaker's disagreement or correct someone else in a somewhat polite manner. He jolly well didn't steal the cookies, I gave them to him.