The question of the right successor to the Prophet Muhammad was answered by the appointment of Abu Bakr, the prophet's general and best friend, as Caliph, or leader.
There were those who believed that Ali should have been named the Caliph. Ali was related to the prophet both by blood and by marriage to the prophet's daughter, Fatima.
Thus the Sunni are those who follow the succession of Abu Bakr and the Shi'a (or Shi'ite) believe that Ali should have been Caliph.
Sunnis are the majority in Islam. Most Shi'a are in Iran / Persia.
There are numerous other sects within Islam. For instance, the famous whirling dervishes are members of the Sunni Sufi.