The Vice President is the office of the government that is responsible for assisting the President of the United States who also acts as president if the president is incapacitated. If the president dies or looses office before he is due for reelection the Vice President takes over. Joe Biden is the current VP under Barack Obama. The very first Vice President was John Adams who later became president.
Dick Cheney is the former vice president. He helped Dubya to stay in office because nobody wanted Cheney as president. It could be argued that one role of the Vice president is to attract attention away from the President. Dick Cheney was extremely good at that. Joe Biden on the other hand...who is he?
The Vice President is also President of the Senate, with his legislative deputy in said upper house being the President pro tempore. While the Vice President presides over the Senate, they don't cast a vote unless to break a tie. The Vice President also swears in new senators.