"Topology is a major area of mathematics concerned with spatial properties that are preserved under continuous deformations of objects, for example, deformations that involve stretching, but no tearing or gluing."To tailor that to the subject, topology is the use of 2D surface shapes positioned at different locations, angles and sizes to create a 3D object. An simple example of this would be a cube. Each face could theoretically count as a plane, 6 planes creating a cube, which when spread out would be the topology of a cube.
The planes can be split up, for example a single square plane can be split up into 4 pieces, creating what is called a subdivision. The cubes topology now has 24 planes, as opposed to 6.
You can continue to create new subdivisions, you could split each of those new 4 pieces into another 4 pieces, creating 16 planes per face... or 96 total planes.
A cube is a very basic example though, when it comes to the topology of the face it is much more complicated. You have different areas containing different sizes and shapes of planes, allowing stretching in certain places for things such as lip and eye movement.
The topology is essentially done around the muscle groups in the face, as you can see comparing the images above and below. You have the forehead & jaw, the cheeks, the eyebrows & cheekbones, the eyes and the nose & mouth. If you put these together in their groups you will have the full topology of the face, ready for manipulation and animating.
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