The voltage reference is what the output is regulated with respect to. If you use a pot, an op amp and a transistor (assuming I'm picturing what you're picturing), the output will always be some fixed ratio to the input. If you use a reference, the output can be fixed no matter what the input does.
Now, typically, a voltage regulator "contains" an op amp (in its block diagram, at least), and the voltage reference is connected to the (+) input, and the output is divided by a voltage divider and that goes to the (-) input. This gives you voltages above the reference voltage. If you move the voltage divider to the reference side, you get voltages below the reference. This topology can be used for the very few times when you need a voltage under 1.2V.
And I suppose the best answer to the "why" would be "almost nothing needs voltages under 1.2V".