Definition of Sufism is, paradoxically, easy and hard to understand at the same time. One of the most important aspects of Sufi character is being pure at heart and straightforward in mind and action. For those who already have this outlook in life, Sufism is something readily apprehensible. On the other hand, the ones whose thoughts are more rampant than their feelings, may find almost every definition unintelligible, or even meaningless.
However, defining Sufism academically, which obviously robs it of its naive charm and somewhat divine authenticity, is not impossible at all. The definition I have found helpful in this regard is this:
Sufism, or Islamic Mysticism, is a subjective attitude of life which puts more emphasis on the chastisement and purification of the inner self, or the Soul, than the doctrinated religious practises and rituals, whatsoever.
This definition may also help us in figuring out the meaning of sufi. The sufi is a man or woman who believes in the Final Testament brought by Prophet Muhammad (Peace Be upon Him), the Messenger of Islam, and tries to adopt his or her life to the Islamic commandments from within rather than from without.