Pastor Aeternus is short and it defines two things, which are often collapsed into one in popular accounts. The first is jurisdiction. The constitution states that the Roman Pontiff has ordinary, immediate and truly episcopal power over the whole Church and over each of its churches and each of its pastors and faithful, and that this power is not merely a right of supervision but a direct authority. In practical terms that is the more far reaching of the two definitions, because it touches the government of every diocese every day.
The second is infallibility, and the text is narrower than it is usually remembered as being. Four conditions are stated together. The pope must be speaking ex cathedra, that is in the exercise of his office as pastor and teacher of all Christians. He must be defining. The subject must be a doctrine of faith or morals. And the definition must be proposed as held by the whole Church. Where all four hold, the definition possesses the infallibility Christ willed for his Church, and is irreformable of itself and not from the consent of the Church.
That final clause, not from the consent of the Church, was the most contested phrase in the document, because it settles a question the councils of the fifteenth century had left open: whether a general council stands above the pope. It does not.