General Relativity describes space-time using the model of a four-dimensional manifold.

In a one-dimensional manifold (or 1-manifold) every point has a neighbourhood that looks like a line. An example of a 1-manifold could be a circle. Wherever you are on that circle, all you can see is a line.

In a 2-manifold, every point has a neighbourhood that looks like a disk. An example of a 2-manifold could be the surface of a sphere. Wherever you are on the surface of that object, all you can see around you is a disk.

The good old balloon model is an example of an expanding 2-manifold. Someone living on the surface of that balloon can only see across the surface, they cannot look up (out of the balloon) or down (into the balloon). They see all points of their universe moving away from them as it expands, but their is no centre of expansion within their universe (the surface of that balloon).

An example of a 3-manifold is a 3-sphere, an object that lives in 4-dimensional euclidean space where every point has a neighbourhood that looks like a sphere. I won't pretend to understand what this object looks like!

If space-time can be modelled as a 4-manifold, I think concepts like the edge of the universe become null and void. Einstein considered that the universe might be finite, but boundless. To me, boundless doesn't mean it goes on forever, it means it has no edge or no bound as space curves back on itself dimensionally. The whole thing expands within itself!