Basically if the following occured:
You get in a war (possibly forced by the AI) and it goes very badly. You have a civilization that has focused on culture rather than military or science, and you are no match for them.
Solution: you surrender and become the AI's vassel. He then stops attacking you, the border tensions are removed, and even though he now can make demands on you, you get to finish building your three culture cities in peace and win the game right under his nose. A similar situation could occur for a religious victory player or even a science player. Being a vassel only really eliminates the possibility of winning via military, dominion, or diplomacy. It could be a nice fallback.