The metaphor, I think, is that your code is a mathematical function, and, to be even more specific and "toy example" about it, let's say it's a polynomial. If the old code was

x^2 + x z + y x + y z

then you notice that you can express the same polynomial as:

(x + y)*(x + z)

It's still the same polynomial, but you "separated concerns", turning it into a product of two simpler factors.

Similar ideas apply to sets of tuples. Perhaps you were given

{(1, 1), (1, 4), (2, 1), (2, 4), (3, 1), (3, 4)}

and you notice that this can be expressed more simply as the Cartesian product:

{1, 2, 3} x {1, 4}

Again, a literal factoring. You can imagine how variations of this idea would apply to database tables and data structures.

That's where I think the word "refactor" comes from.