What was the essential dispute between Islam over the succession of the prophet?

After, Prophet Muhammed's death, a majority of the people thought Abu Bakr was the rightful successor of Prophet Muhammed because he was his best friend and others thought Ali, Prophet Muhammed's son-in-law was the rightful successor. Though Ali didn't partake in this dispute and waited for his turn, there was and is a division among the Muslims and now there are two main groups, Sunnis who believe that all four caliphs (Abu Bakr, Umar, Uthman) and Ali) were the rightful successors and the Shiites or Shi'as who believe only Ali was the rightful successor.