It is possible to refactor the semantics (denotative meaning) of a work. However, natural language isn't limited to semantics (or functionalism). It contains connotative meaning as well, normally called style (e.g. rhetoric). The style of a text comes from the structure of the writing, the relationship of the words. It is strictly not possible to refactor a piece of writing and preserve the style.
Consider the difference between, "Quickly, John ran to Jane." and "John ran quickly to Jane." Functionally the two sentences are equivalent, but stylistically they are quite different. The first sentence emphasizes the speed at which John ran whereas the second (more weakly) emphasizes the characters in the narrative.
But more practically, refactoring text is really rare (although it is possible say by moving a section of discussion to a separate page on a wiki). Rewriting is much more common. Restating what was said, removing what's not interesting, explaining points in further detail.
So, when someone says they are refactoring a page, they are more likely to be rewriting it so it reads better.
A big goal when rewriting is to preserve the relationship of the text under revision to other works in the system. Thus, when rewriting a page on a wiki, one doesn't want to have to adjust the relationships it has to other pages. (This could be false if the discussion becomes meta, but we'll ignore those cases because they are self-defeating anyway.)
Think about renovating a basement bathroom in the house. A good contractor can do the job without changing the upstairs bedrooms. A really good contractor may not even affect the surrounding rooms.
See also ReworkingProblems.
This page is a simple rewrite of WhatIsReworking with the intent of moving from "reworking" (a term applied to a material that is to be worked on again, usually due to defects arising during the first attempt) to "rewriting" (the correct term). I fully intend to continue the transition at a later stage, unless opinion solidifies against the decision. -- ChrisPurcell