Thanks Viktor for asking. Not everything can be defined. Sufi idea is one such thing. You can't define Divine Love, can you ? (but u can realize it, u can atleast try to explain it with certain limitations). You have to realize the truth in your heart cause its so subtle and at the same time, so grand, words are not enough.
To make things clear at first, Sufi Idea is NOT faith. Sufism is philosophy among the religions and it is a religion among the philosophies. It is realization of God, devotion and love. It is not a successor to Islam, but it continues even after Islam.
Sufis are mystics and the central idea of Sufism is believed to have existed from the beginning of creation. All Messengers, Biblical Prophets are Mystics. Traces of Sufism or Mysticism are to be found in all periods of History. Abraham, Moses, Jesus propagated the Divine Love, Sufism until the coming of Muhammad, by whom this Brotherhood was formed, while it is advanced by Ali and later spiritual personalities.
The Sufi sees the truth in every religion. They understand the hidden message in all faith because each are longing for the same goal, uniting with the Ultimate Soul, God, Heaven in Father who created Man in His own image, with His own Spirit.
If invited to offer prayers in a church, a mosque, a synagogue, or a temple, the Sufi is ready to do so, knowing that all people worship the same God, the Only Being, no matter what Name they use. Yet the Sufi's true house of worship is the human heart, in which the Divine Beloved lives.
Sufism is a religion for those who wish to learn religion from it, a philosophy for those wanting wisdom from it, a mystical path for any who would be guided by it to the unfoldment of the Soul, and yet it is beyond all these things. It is the Light of Life, which is the sustenance of every soul. Sufism is the Message of Love, Harmony, and Beauty
The tendency of the Sufi is to unite humanity than to differ. That is why they readily appreciate and seek the inner beauty of the teachings of all spiritual leaders becaues all souls are inspired by the One God. Not distraced by the outer differences but able to seeing the inner reality, they can transcend beyond any forms, culture, language and even religious faith.
Sufism is the ancient school of wisdom. The Mysticism that was only taught to very close disciples of Jesus and also Muhammad are often quoted inspirations. If you are seeking to undestand life and yourself, then you can call yourself Sufi. Every seeker after the ultimate truth is really a Sufi.
For more detail, you can read from the following links,
I may go on quoting many things about Sufi, but its better to leave it to you to discover more.
Surely all inspirations come from our Beloved God and He only shows the path whoever seeks for it. As Jesus said, "I say unto you, ask, and it shall be given you; seek, and ye shall find; knock, and it shall be opened unto you".