"a papal document treating of matters related to the general welfare of the Church, sent by the Pope to the bishops. 
Used especially in modern times to express the mind of the Pope to the people.  Although of themselves not infallible documents,
encyclicals may (and generally do) contain pronouncements on faith and morals that are de facto infallible because they express
the ordinary teaching of the Church.  The faithful are to give the papal encyclicals there interior assent and external
respect as statements of the Vicar of Christ".  (Catholic Dictionary- Fr. John Hardon, S.J.)