Takfiir is an Arabic word and it means, more or less, excommunication. Now there are differences between the two ideas. Technically, excommunication means to ban a person from Communion, seen as the central ritual and sacrament of the faith.
Now you have probably heard the word "kaafir" which is often translated "unbeliever." That word is derived from kafara which means "(he) became an unbeliever." Then there is the word (with two f's) and has a causative meaning, "kaffara," which means "he excommunicated." Takfiir is the gerund of that verb. The person who has become kaafir has surrendered his personal security under Islamic law.
If there is one novelty in OBL's practice of Islam, it surrounds takfiir. By using takfiir very liberally he expands the number of people who can be killed in jihad. Very nicely explained here:
The concept of takfir, or excommunication, coupled with the mandate to kill unbelievers (Qur'an 9:5) leads to two internal consequences for Muslim communities: One is eternal instability, as tempers are conditioned to be short and explosive over disagreements. Additionally, the lack of separation of religion and state in Islamic teachings only adds fuel to the fire where political disagreements arise, demonstrated by both Shi'ites and Sunnis in this article.
In that atmosphere, the hazards of being branded a substandard believer, coupled with the military and material incentive for demonstrating religious devotion only further encourages as literal a following of texts and teachings as possible (see also: Gaza Strip). And thus, there arises a self-perpetuating cycle in that the solution to Islamically-charged instability is always more Islam (since the root of the problem is that the other party has it wrong), more sharia, and more jihad to make it happen.
From Here.
