What is an Encyclical?

A Papal Encyclical is the name typically given to a letter written by a Pope to a particular audience of Bishops. This audience of Bishops may be all of the Bishops in a specific country or all of the Bishops in all countries throughout the world. 

A more complete description can be found in the Catholic Encyclopedia entry Encyclical:

"According to its etymology, an encyclical (from the Greek egkyklios, kyklos meaning a circle) is nothing more than a circular letter. In modern times, usage has confined the term almost exclusively to certain papal documents which differ in their technical form from the ordinary style of either Bulls or Briefs, and which in their superscription are explicitly addressed to the patriarchs, primates, archbishops, and bishops of the Universal Church in communion with the Apostolic See. By exception, encyclicals are also sometimes addressed to the archbishops and bishops of a particular country."

The 1917 Catholic Encyclopedia entry on Bulls and Briefs further explains other papal documents:

"In official language papal documents have at all times been called by various names, more or less descriptive of their character. For example, there are "constitutions," i.e., decisions addressed to all the faithful and determining some matter of faith or discipline; "encyclicals," which are letters sent to all the bishops of Christendom, or at least to all those in one particular country, and intended to guide them in their relations with their flocks; "decrees," pronouncements on points affecting the general welfare of the Church; "decretals" (epistolae decretales), which are papal replies to some particular difficulty submitted to the Holy See, but having the force of precedents to rule on all analogous cases. "Rescript," again, is a form applicable to almost any form of Apostolic letter which has been elicited by some previous appeal, while the nature of a "privilege" speaks for itself. But all these, down to the fifteenth century, seem to have been expedited by the papal chancery in the shape of bulls authenticated with leaden seals, and it is common enough to apply the term bull even to those very early papal letters of which we know little more than the substance, independently of the forms under which they were issued."