The First Vatican Council was when a bunch of Catholic leaders got together to talk about what it means to be Catholic, what the Church teaches, and how the Church should govern itself. It happened a long time ago, in the 1800s.
One thing they talked about was the idea of papal infallibility, which means that the pope (who is like the boss of the Catholic Church) can't make mistakes when it comes to matters of faith and morals. This means that when the pope speaks "ex cathedra" (which is a fancy way of saying "from the chair" because he's sitting on a special chair), he's always right.
Another thing they talked about was the hierarchy of the Church, which is like a big pyramid. At the top is the pope, then bishops, then priests, and then the regular people (like you and your family). They talked about how this hierarchy should be organized and how everyone should be on the same page when it comes to what the Church teaches.
Overall, the First Vatican Council was a big meeting where Catholic leaders talked about what it means to be Catholic and how the Church should work. They talked about papal infallibility and the hierarchy of the Church, and they made some important decisions that still affect the Church today.