Bismillaah-ir-Rahmaan-ir Raheem.

Assalaamu 'Alaykum wa Rahmatullaahi wa Barakaatuh.

Tasawwuf is the science of the path to Allaah. Tasawwuf or Sufism is an important branch of Islam, pertaining to the reformation of the self (nafs). It consitutes of purifying the heart of spiritual ailments and illuminating it with the Noor (light) of Divine Love. The aim of a Saalik (the one who adopts tasawwuf) is to create a connection of love with Allaah, and gain His pleasure., sacrificing his own desires for the pleasure of His creator. Just as the Horizon turns red before the sun rises to illuminate the world. Similarly, when the Saalik colours his heart with the red blood of his slain desires, the sun of Allaah's love rises in his heart, and illuminates his world.

Please take the time to read the articles found on the following two links for farther explanation:

http://www.cislamonline.com/library/index.php?view=tasawwuf/whatis

http://www.cislamonline.com/library/index.php?view=tasawwuf/new

Jazakallaah.

And Allaah knows best.

Wassalaam.