http://w.astro.berkeley.edu/~converse/rubiks.php?id1=basics&...
A commutator is any sequence of moves in the form of A B A' B', where A and B are sets of moves, and A' and B' are those sets of moves undone. So this example basically just restricts B to consist only of top-layer moves.
If you want to take the arrows very literally, you can think of the commutator as measuring the amount of curvature in the space the arrows lie in. The less of a difference the commutator makes, the less curved - with a commutator that doesn't do anything meaning the space is flat. Expressed in these terms, the two-part algorithm technique amounts to finding places in Rubik's cube algorithm space that are almost – but not quite – flat.
To me, it's much more satisfying than memorizing/learning existing solutions, even though I'll never be as fast as those that do leverage those solutions.
Either way, though, I'd recommend buying an inexpensive "speed cube" from Amazon, they are much less frustrating than the original design. (It doesn't bind up in the middle of a transformation.)
It showed me that intuition only goes so far, beyond a point one has to put in some serious hard work (memorize patterns/algos etc) to see how deep one can go in any field.