Sufism is the name of the religion that Sufis practice. Sufism is a mystical variation of Islam.
By practicing Sufism, Sufis seek to have a close, personal experience of God. Sufism is less a sect or split from Islam, and more of an aspect of the Islamic religion — Sufis also consider themselves to be Muslim, and like any devout Muslim, they pray five times a day and follow the teachings of Muhammad. Sufism simply includes more mysticism and rituals, like the spinning dance done by "whirling dervishes." In Arabic, Sufi means "man of wool."