I'm always a little leery of definitions because everyone has his or her own, but when you write a book you get to choose your own definitions. In this case I'm basing my definitions on the work done by Ralph Johnson's group and assorted associates.
The first thing to say about this is that the word Refactoring has two definitions depending on context. You might find this annoying (I certainly do), but it serves as yet another example of the realities of working with natural language.
The first definition is the noun form.
Refactoring (noun): a change made to the internal structure of software to make it easier to understand and cheaper to modify without changing its observable behavior.
You can find examples of refactorings in the catalog, such as Extract Method and Pull Up Field. As such, a refactoring is usually a small change to the software, although one refactoring can involve others. For example, Extract Class usually involves Move Method and Move Field.
The other usage of refactoring is the verb form
Refactor (verb): to restructure software by applying a series of refactorings without changing its observable behavior.
So you might spend a few hours refactoring, during which you might apply a couple of dozen individual refactorings.
I've been asked, "Is refactoring just cleaning up code?" In a way the answer is yes, but I think refactoring goes further because it provides a technique for cleaning up code in a more efficient and controlled manner. Since I've been using refactoring, I've noticed that I clean code far more effectively than I did before. This is because I know which refactorings to use, I know how to use them in a manner that minimizes bugs, and I test at every possible opportunity.
I should amplify a couple of points in my definitions. First, the purpose of refactoring is to make the software easier to understand and modify. You can make many changes in software that make little or no change in the observable behavior. Only changes made to make the software easier to understand are refactorings. A good contrast is performance optimization. Like refactoring, performance optimization does not usually change the behavior of a component (other than its speed); it only alters the internal structure. However, the purpose is different. Performance optimization often makes code harder to understand, but you need to do it to get the performance you need.
The second thing I want to highlight is that refactoring does not change the observable behavior of the software. The software still carries out the same function that it did before. Any user, whether an end user or another programmer, cannot tell that things have changed.
The Two Hats
This second point leads to Kent Beck's metaphor of two hats. When you use refactoring to develop software, you divide your time between two distinct activities: adding function and refactoring. When you add function, you shouldn't be changing existing code; you are just adding new capabilities. You can measure your progress by adding tests and getting the tests to work. When you refactor, you make a point of not adding function; you only restructure the code. You don't add any tests (unless you find a case you missed earlier); you only restructure the code. You don't add any tests (unless you find a case you missed earlier); you only change tests when you absolutely need to in order to cope with a change in an interface.
As you develop software, you probably find yourself swapping hats frequently. You start by trying to add a new function, and you realize this would be much easier if the code were structured differently. So you swap hats and refactor for a while. Once the code is better structured, you swap hats and add the new function. Once you get the new function working, you realize you coded it in a way that's awkward to understand, so you swap hats again and refactor. All this might take only ten minutes, but during this time you should always be aware of which hat you're wearing.