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 Latinencyclicus (from the Greekἐν κύκλῳen kykloi) meaning "general" or "encircling", which is also the origin of the word "encyclopedia".
For the modern Catholic Church a Papal encyclical, in the strictest sense, is a letter, usually treating some aspect of Catholic doctrine, sent by the Pope and addressed either to the Catholic bishops of a particular area or, more normally, to the bishops of the world; however, the form of the address can vary widely, and often designates 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. Papal encyclicals are so famous that the term encyclical is used almost exclusively for those sent out by the Pope. The title of the encyclical is usually taken from its first few words (its incipit).
Within Catholicism in recent times, an encyclical is generally used for significant issues, and is second in importance only to the highest ranking document now issued by popes, an Apostolic Constitution. However, the designation 'encyclical' does not always denote such a degree of significance. The archives at the Vatican website currently classify certain encyclicals as Apostolic Exhortations. This informal term generally indicates documents with a broader audience than the bishops alone.
Pope Pius XII held that Papal Encyclicals, even when they are not of 'ordinary magisterium', can nonetheless be sufficiently authoritative to end theological debate on a particular question:
It is not to be thought that what is set down in Encyclical letters does not demand assent in itself, because in this the popes do not exercise the supreme power of their magisterium. For these matters are taught by the ordinary magisterium, regarding which the following is pertinent: “He who heareth you, heareth Me.” (Luke 10:16); and usually what is set forth and inculcated in Encyclical Letters, already pertains to Catholic doctrine. But if the Supreme Pontiffs in their acts, after due consideration, express an opinion on a hitherto controversial matter, it is clear to all that this matter, according to the mind and will of the same Pontiffs, cannot any longer be considered a question of free discussion among theologians.
^Allocution to the Cardinals AAS 1946, 141, and, AAS 1952, 5, AAS 1955, 15; and, for example in his Christmas Message 1954, AAS, medical doctors on the use of modern weapons, AAS 1954, 587, farmers, AAS 1950, 251, fashion AAS 1957, 1011, human dignity, AAS 1951, 215, AAS 1957, 830