Subdivision

Subdivision generates a smoother, higher resolution mesh which is based on the geometry of the base mesh, and updates when you make changes to the base mesh. To get a quick idea of subdivision does, create a cube or some other shape and then press C one or two times to Subdivide. Try selecting some of its faces, and you will see that even though the cube has been subdivided, you are still actually working with the geometry of the original cube. Press V a few times to Unsubdivide.

Subdivide - C

       Subdivide creates a smoothed version of an object underlying the original object. Edits applied to the original polygon mesh will affect the subdivided shape. This operation can be performed multiple times to create a smoother underlying shape. You can use the Paint Displacement tool to displace the smooth subdivided surface using brush tools.

Unsubdivide - V

       If an object has been subdivided, Unsubdivide goes back one level of subdivision. This can be performed until there is no underlying subdivided shape.

Refine Control Mesh - Shift + C

       Refine Control Mesh deletes the polygonal control mesh and makes the underlying subdivided shape directly editable.

Crease Edges

       Crease Edges makes the subdivided shape more closely conform to the control mesh along the creased edges. Creased edges cannot be exported to other applications, unless you refine the control mesh.

Uncrease Edges

       Uncrease Edges removes creases (if applied) from the selected edges.