Takfir is the act of declaring another Muslim to be an unbeliever. It is not merely an insult. Under classical rulings an apostate may lawfully be killed, so a declaration of unbelief is the doctrinal move that converts a disagreement between Muslims into a licence to shed blood, and it was being used for exactly that purpose by armed groups in the years around the turn of the century.
The Amman Message was issued in November 2004 and put to an international gathering of scholars in July 2005. Two hundred scholars from more than fifty countries took part, and what they produced has three parts. First, eight schools of Islamic law are named as valid: the four Sunni schools, together with the Jafari and Zaydi Shia schools, the Ibadi school and the Zahiri school. Second, whoever follows any of the eight is a Muslim, and declaring such a person an unbeliever is forbidden. Third, the conditions for issuing a fatwa are specified, so that a ruling from someone without the qualifications carries no weight.
The third point is the least quoted and does much of the work. Most of the takfir being issued was coming from people with no standing to issue anything, and setting out who may give a legal opinion attacks the practice at its source rather than at its conclusion.
The declaration also names Ashari theology, genuine Sufism and true Salafi thought as within Islam, which was a deliberate refusal to let the argument be conducted as one tendency against another.