It's called "Target Fixation", Dan. One tends to drive/ride toward any focused-upon point ahead of them. It's similar as in situations where you spot a pothole ahead of you and continue to focus upon it while thinking you must avoid it, but then find you're strangely "attracted" to it and ultimately find yourself rolling over it.
But, this phenom can of course also be used in a positive manner, such as the situation you described with your figure-8 exercise, or when riding around a twisty road and remembering to keep your head turned and somewhat craned up and focusing your sight as far up around the turn as you can see, which as you said will automatically(and in a way, "magically") have you and your bike making sharper turns, and with much less a chance of "going wide".
