Encyclical
An encyclical was originally a circular letter sent to all the churches of a particular area in the ancient Roman Church. At that time, the word could be used for a letter sent out by any bishop. The word comes from Late Latin encyclios (from Latin encyclius, a Latinization of Greek ἐγκύκλιος enkyklios meaning "circular", "in a circle", or "all-round", also part of the origin of the word encyclopedia).
The term has been used by Catholics, Anglicans and the Eastern Orthodox.
Catholic usage
For the modern Catholic Church, a Papal encyclical is a kind of letter concerning Catholic doctrine sent by the Pope addressed to bishops, patriarchs, primates, and archbishops who are in communion with the Holy See. The form of the address can vary widely, and may concern bishops in a particular area, or designate a wider audience. Papal encyclicals usually take the form of a papal brief due to their more personal nature as opposed to the formal papal bull.
Although the term "encyclical" originally simply meant a circulating letter, it acquired a more specific meaning within the context of the Catholic Church. In 1740, Pope Benedict XIV wrote a letter titled "Ubi Primum", which is generally regarded as the first modern-sense encyclical. The term is now used almost exclusively for a kind of letter sent out by the Pope. Encyclicals are usually written in the Latin language, and the title of the encyclical is usually taken from its first few words (its incipit).