In the field of software design, refactoring means reorganising existing code to make it more readable, without changing its behaviour. Externally the program does the same thing, but internally it’s all sparkling clean and polished.

A (not very good) non-software example would be this:
BEFORE:
(1 + (1 + 1 + 2) + 1 + 3) * ((1 + 1) + 2)
AFTER:
9 * 4

The end result of both is 36, but the second one is much clearer and easier to read.

Educate us – what’s refactoring?