Here is a possible way to think about a closed surface or to test if a surface is closed.
By definition, in simple terms, a closed surface should contain some volume. This volume could be filled with some material (rock) or it could be, roughly speaking, empty (ping pong ball).
So, here is the test that should hold for a closed surface: if you are inside the volume contained by a closed surface, you cannot get out and, if you are outside that volume, you cannot get in - without breaking through the surface.
For instance, if you take a sealed cylindrical tin can, you cannot get anything out or insert anything in without making a hole in its surface or opening it. So, this is an example of a volume contained by a closed surface.
If you take a piece of a (cylindrical) PVC pipe, you can put things inside the pipe and take them out without breaking through its surface. So, we can say that the outer surface of the PVC pipe is not a closed surface, because it does not seal the volume inside the pipe.
On the other hand, if we look at the volume inside the walls of a PVC pipe, we can say that this volume is fully contained by total surface of the pipe, which includes the outer surface, the inner surface and the surface of the edges at the two ends of the pipe. You cannot insert anything into the walls of the pipe without breaking that surface somewhere. So, from this perspective, the surface of this cylindrical pipe is closed.
You can try to use this approach with other objects and see if it helps differentiate closed surface from non-closed surfaces.