What is the most important job of the vice president?

The Vice President has the power to break a tie vote in the Senate. This is the only actual power he has and on occasion it has been important. His real function is to be able to seamlessly step into the Presidency if something happens to the President. It is not really a job and there is not much he needs to do to prepare since it will probably never happen, but if its does, it is tremendously important.