Takfirist is a term used to describe some terroristic Islamic groups by their Arab opponents. The word means literally "excommunicator", and you are likely to find it on the lips of all of al-Qaeda's enemies in the Arab world - from the secular regime in Syria to Iraq's Mehdi Army. The word derives from the practice of groups like al-Qaeda of declaring all Muslims who do not follow their strict worldview to be excommunicated from Islam - to be, in effect, non-Muslims. The belief held by al-Qaeda that the only true Muslims are themselves is what gives them wide latitude to murder Muslims in pursuit of their goals, as they have done in far greater numbers than they have murdered non-Muslims.
Takfirism is an offshoot of Salafism, on which we have recently received an excellent write-up. Salafism is a political movement which aims to restore conditions on Earth to those that existed at the time of the Prophet Mohammed. In its most benign forms, it drives believers to form small, isolated communities where they can pursue this simple life. Takfirists, on the other hand, seek to violently bring about these conditions on the whole Earth through a political and military strategy.
Takfirists consider themselves to be a vanguard party, the only true representatives of Islam on Earth. They see the rest of the world as being in a state of Jahiliyyah, or "ignorance of divine guidance"; this is the term commonly applied in the Qu'ran to the time on the Arabian peninsular before the birth of the Prophet Mohammed. As such, Takfirists envisage their goal as similar to that of the Prophet and his early companions - bringing true religion to a pagan world. In their eyes, other so-called "Muslims" have strayed from the divine path - often, have been led astray by the West and the secular Arab regimes the West backs - and, for as long as this remains the case, they are enemies.
Takfirism is inherently violent because of the radical difference between the world as they wish it to be, and the world as it actually is. In this respect they resemble ideological movements like Nazism and Bolshevism - the change they want to bring about in the world is so radical, so far-reaching, that in the first instance all there is for them to do is destroy. The worse it gets, the better it is - the more damage they can inflict on the world as it is now, the weaker and more susceptible to change it will become.
Hence, the main duty incumbent on Takfirists is jihad - the waging of war against all forms of non-Takfiri authority, which in practice means the United States of America and Arab regimes such as Iraq and Egypt. Shi'ites are also a prime target for Takfirists, as became clear in the early days of the Iraqi civil war - the formation of Shia self-defence organizations like the Mehdi Army was explicitly aimed at Takfirists who were at the time randomly bombing Shia districts of Baghdad.
Takfirist ideology gives a huge amount of scope for acts that would otherwise be considered contrary to Islam because of the primacy of jihad. al-Qaeda members who subscribe to these views hence excuse drinking alcohol, taking drugs, eating proscribed foods such as pork, and shaving their beards as necessary measures to blend in to Western societies to carry out terrorist attacks. Suicide is also excused, despite the Quranic injunction that those who commit suicide are condemned to forever repeat their final act in Hell - to Takfirists, this act is also excused in the name of jihad, and will instead send the perpetrator to Paradise.
Iraq is the place in which we have mostly recently witnessed a Takfirist war against their fellow Muslims. Iraqi Shia and non-Takfirist Sunnis were by far the biggest victims of al-Qaeda in Iraq's bombing campaigns, and their actions eventually became so distasteful to the mainstream of Iraqi Sunnis that the latter flocked in droves to the Americans to help them form self-defence organizations to drive the Takfirists out. This has now largely been accomplished, and is part of a broader trend of the apparent loss of legitimacy suffered by Takfirists across the Islamic world. To take another example, the popularity of Osama bin Laden and the Taliban in Pakistan plummeted after the assassination of Benazir Bhutto.
Takfirism can never be successful in winning over anything but a small minority of Muslims to its cause because of its radical and violent nature. Takfirists have never managed to erect any positive political monument, never created one of their utopian communities or even succeeded in delivering a crippling blow to an Arab regime or a Western power. All they have delivered is dead Muslims. They are now being outflanked by Iranian-backed Shia groups, their arch-foes, who at least have a programme of political action - however distasteful it may be - rather than seeking merely to kill and destroy. Takfirism will never be eliminated altogether, but one of the unexpected consequences of the war in Iraq is that its moral bankruptcy is now plain for the Muslim world to see. Whether this was worth the tremendous cost is left as an exercise to the reader.