Confusion about fiber product in the category of categories.

Question

The Beauville-Laszlo theorem is a classical result in algebraic geometry. On wikipedia https://en.wikipedia.org/wiki/Beauville%E2%80%93Laszlo_theorem there is a global version of it and it is stated that a certain diagram is a pushout. But the maps are between categories there and given by the restriction of vector bundles. Does this mean that it is a pushout in the category of categories and what does it mean? I know that the idea is that a vectorbundle on an algebraic curve can described by its restriction to a small neighborhood around a rational point and to the curve without that point. But what does it mean formally. Thanks!