Sufism:
Sufism or taṣawwuf (Arabic: تصوّف) is defined by its adherents as the inner, mystical dimension of Islam. A practitioner of this tradition is generally known as a ṣūfī (صُوفِيّ). Sufis believe they are practicing Ihsan (perfection of worship) as revealed by Gabriel to Muhammad, “Worship and serve Allah as you are seeing Him and while you see Him not yet truly He sees you.”
Classical Sufi scholars have defined Sufism as “a science whose objective is the reparation of the heart and turning it away from all else but God”. Alternatively, in the words of the DarqawicSufi teacher Ahmad ibn Ajiba, “a science through which one can know how to travel into the presence of the Divine, purify one’s inner self from filth, and beautify it with a variety of praiseworthy traits”.
Some mainstream scholars of Islam define sufism as simply the name for the inner or esoteric dimension of Islam.René Guénon in Insights into Islamic Esoterism and Taoism (Sophia Perennis 2003) contended that Sufism was the esoteric aspect of Islam supported and complemented by exoteric practices and Islamic law. However, according to Idries Shah, the Sufi philosophy is universal in nature, its roots predating the rise of Islam and the other modern-day religions, save for perhaps Buddhism and Jainism; likewise, some Muslims consider Sufism outside the sphere of Islam.

Islam and Sufis:
Sufism is commonly called the mystical branch of Islam, but many Sufis would argue the point, saying that Sufism existed before the advent of the Prophet Mohammed. This perspective makes Sufism a non-dogmatic tradition of devotion and mystical technology, somewhat parallel to the role of Yoga in India. Others, however, find this argument offensive, asserting that Sufism is well-rooted within the religion of Islam. Either way, it is a holy well of sacred experience and has inspired some of the finest mystical poetry given to the world.

The Sufis:
Sufis are sometimes called the Masters of Love because the Sufi path strives for ecstatic ego annihilation in the fires of Divine Love.

The origin and meaning of the word Sufi is often debated. It is often said to derive from the Arabic word for wool (suf), and a reference to the simple, rough clothing often associated with early Muslim ascetics. Other possible meanings for the term relate to purity, the chosen ones, even a reference to the Greek word for wise man (sophos). The truth is that all of those possible meanings tell us something of what it means to be a Sufi.

The Sufi commentator Qushayri gives a beautiful description of the Sufi ideal:

Sufism is entry into exemplary behavior and departure from unworthy behavior.
Sufism means that God makes you die to yourself and makes you live in him.
The Sufi is single in essence; nothing changes him, nor does he change anything.
The sign of the sincere Sufi is that he feels poor when he has wealth, is humble when he has power, and is hidden when he has fame.
Sufism means that you own nothing and are owned by nothing.
Sufism means entrusting the soul to God most high for whatever he wishes.
Sufism means seizing spiritual realities and giving up on what creatures possess.
Sufism means kneeling at the door of the Beloved, even if he turns you away.
Sufism is a state in which the conditions of humanity disappear.
Sufism is a blazing lightning bolt.
(quoted in Sufism: An essential introduction to the philosophy and practice of the mystical tradition of Islam, by Carl W. Ernst, PhD)

Though not as widely known or practiced in the West today as Yoga, Sufism has had a profound effect on the mystical traditions of the world, both East and West, since the Middle Ages. The Sufi tradition seems to have influenced developments in modern Yoga, particularly the ecstatic devotional practices of Bhakti Yoga. In Europe, as well, where mysticism often had to remain underground and look for mystical traditions “lost” or suppressed in mainstream expressions of Christianity, the Sufis greatly inspired Christian mystics, reaching them through Moorish Spain, through the interaction of the Crusades, and through the influence of Islamic physicians and scientists in service at various European courts.

Sufi Poetry

Poetry has been a revered art in every world culture, but this is particularly so throughout the Islamic world. This is partly due to the traditional Islamic prohibition on representational art. Since portrayal of people and things was largely forbidden, the visual arts tended to focus on rich, elaborate patterns and calligraphy, while much of the Islamic artistic genius emphasized the power of words over the visual image. And the Quran itself uses highly poetic language which, of course, inspires a tendency among Muslims to express themselves in a similarly poetic fashion. Perhaps the desert environments that predominate in many Islamic countries likewise contributed to a vocal rather than a visual focus.

The poetic tradition within Islam, still very much alive today, has given us an amazing bounty of sacred and mystical poetry from the Sufi and Muslim traditions.

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References:
http://en.wikipedia.org/wiki/Sufism
http://www.poetry-chaikhana.com/Traditions/MuslimSufi.htm
http://en.wikipedia.org/wiki/History_of_Sufism