An apostolic exhortation is a magisterial document written by the pope. One could argue it ranks third in importance, after apostolic constitutions and encyclicals.
It's essentially a pastoral message the pope sends out to Catholics to highlight key points about a particular issue.
Usually the Pope writes apostolic exhortations after consulting with bishops who participate in relevant synods. But that's not always the case.
An apostolic exhortation establishes a clear direction for Catholics to critically address issues that are being discussed within the Church and in modern society.