So, a papal apocrisiarius is a fancy name for someone who is the pope's ambassador. It's like when mommy or daddy sends you to give a message to your neighbor or a teacher. The pope is like the big boss of the Catholic church, and he has to talk to other leaders in different places about important things.
But the pope can't always travel to these faraway places, so he sends someone to go in his place. That person is the papal apocrisiarius! They are like a messenger for the pope, and they speak on behalf of him. They also help the pope learn about what is happening in other countries, so he can make good decisions for the church.
So, the papal apocrisiarius is like a special representative for the pope, who travels to different places to help spread the word of the church and make the pope's voice heard.