It's an open letter from the pope. An encyclical will often clarify Church doctrine on a topic, or set of topics. See e.g. Humanae Vitae[1] for an example of one that has resulted in, essentially, a lay rebellion — at the time it was issued many clergy, including Bishops opposed it, but the Church itself has gradually become far more conservative (perhaps as a reaction to Vatican II) in the intervening years.

1: https://en.wikipedia.org/wiki/Humanae_vitae