Electric charge is a slippery thing. You can measure how much there is in the entire universe or in a single particle, but try to point your finger and say, 'Right here, in this cubic centimeter, there is exactly this much charge right now,' and you hit a fundamental wall.
The issue is that total charge, which physicists denote by the letter Q, is nonlocal. It's like trying to determine exactly where in an orchestra the melody is born: it's everywhere and nowhere in particular. Usually, to describe charge flows, physicists use the current operator — a set of four numbers showing how much charge flows through a unit area per unit time. But strictly defining this operator in our three-dimensional world plus time (so-called Minkowski space) has proven to be no easy task. In a two-dimensional world, it's a different story — the math is simpler.
Imagine a flashlight that doesn't illuminate the whole room at once, but only a circle on the wall. The total light from the bulb is analogous to the total charge Q, and the spot on the wall is the 'charge with a region of action.' By changing the shape and size of the spot (that is, the projection), we can study charge at different scales without losing the big picture. And although we are still far from a final answer to 'what is charge?', this perspective helps bring into focus what was once just a blurry blob.
In quantum field theory, a particle's charge is not an intrinsic property but arises from its interaction with the field, like ripples on water from a thrown stone.