One-handed typing is a euphemism for computer-assisted sexual activity (no prizes for guessing what the other hand is occupied with). It's also a useful skill, allowing one to type while holding something (a cigarette, a telephone, a baby, etc.) in the other hand. With a laptop, one-handed typing offers the ultimate computer extravagance - internet while lying in bed1. Aside from all these (debatably) useful applications, one-handed typing is a useful way to improve your typing proficiency
If you type in the 'hacker style', typing one handed can greatly improve your 'muscle memory' of the keyboard, greatly increasing your typing speed (if you've been trained in touch typing, it will likely hinder more than it helps). The reasons it helps hacker-style typing are two-fold: Firstly it gives you half the number of fingers to play with, so you'll have to move these fingers twice as fast to keep up the typing speed you're used to.
Secondly, the posture is different for one-handed typing - When typing with two hands, your wrist stays still (it rests on something (like the table or an wrist cushion) if you're bad, or hovers over the keyboard if you're good), and your fingers bunch up. To type one handed, your hand must spread out (increasing the effort required to depress the key), and your wrist must move back and forth across the keyboard. You'll quickly discover that the more fingers you use, the less your hand needs to move about, and the longer you can type without tiring your arm out. The increased effort required to press the keys should give your fingers good exercise, making them faster and stronger.
With practice, you should find yourself using your weaker fingers (ring fingers and pinkies) more often, and the speed with which you can move a finger from one key to another increasing dramatically.
Once you're used to typing with one hand, it's a small step to move to typing with two hands at twice the speed you used to.
1 - This W/U typed with my right hand, while lying in bed.