You can refine any mesh that has a level of smoothness of 1 or higher.

Refine a Mesh Object and Reset the Baseline

Refining an object increases the number of editable faces by converting the underlying
facets to faces. The number of resulting faces depends on the current level of smoothness.
Higher smoothness levels result in a higher number of faces after refinement.

In addition to increasing the number of faces, refining a mesh object resets its level
of smoothness back to the baseline. Therefore, an object might appear to be smoothed,
but its smoothness level can still equal 0 (zero).

Refine a Mesh Face

You can refine an entire mesh object as shown in the previous illustration, or select
a specific face to refine. A refined face is subdivided into four faces and the surrounding
faces are deformed slightly to accommodate the change.

Refining a mesh face does not affect the overall smoothing level of the mesh object.
Unlike a refined mesh object, refined faces can be refined again immediately. With
mesh face refinement, you can target smaller areas for detailed modeling.

How Refinement Affects Creases

A crease that is set to Always retains its sharpness no matter how much you smooth
or refine the object. However, the behavior is different when you assign a crease
value. If you refine an object or edge that has a crease value, the assigned crease
value is lowered by the value of the original level of smoothing. Suppose that you
add a crease with a crease value of 4 and then refine a mesh whose level of smoothness
is 2. The new crease value is 2.

If a crease is applied before an object is smoothed or refined, the effect is not
apparent until after the object is smoothed or refined.