When objects and shapes are created, each vertex and/or face is assigned a number. These numbers are used internally to determine which vertices or faces are selected at any given time. This numerical arrangement is called topology.

When you select vertices or faces and apply a modifier to the selection, the modifier stack keeps track of which faces/vertices the modifier affects. If you later return to the selection level of the stack and change the selection, you change the topology to which the modifier is applied.

The term topology refers to the structure of faces and vertices as well as their numbers.