In 3D modeling, the term topology refers to a 3D model's edge distribution and structure. Two models that look the same when rendered can have very different topologies.
Two different topologies that result in the same rendering
The model on the top is constructed mostly with quads (four-sided polygons) while the model on the bottom is constructed with triangles (three-sided polygons), also known as tris. These models are said to have different topologies.
Topology affects many aspects of 3D modeling and rendering, including:
How highlights react to the model
How easy it is to edit the model's shape
How easy it is to apply or edit mapping. Unwrapped UVs are easier to manage with quad topology.
How easy it is to rig and animate the model. Quad topology makes it much easier to rig and animate.