Here's another useful reference article.
A lot of beginner car enthusiasts have trouble understanding differentials, both regular and limited-slip ones. In fact it is a very simple device. So simple in fact, that the first vehicle that is considered in modern terms a car, the Mercedes Simplex of 1903, was distinguishable from other self-propelling carriages by the fact that it had one. (Among other things.)
The differential is a part that splits torque, usually into two equal parts. It has an input shaft and two output shafts, one per each wheel (or axle if it's the central diff in an AWD car). Now, when a car turns, the outer wheels take a wider curve than the inner ones, covering more distance and thus traveling at a higher speed. This happens because the axles have differentials, as opposed to just solid pieces of metal connecting the two wheels.
The differential is made up of gears. The input shaft has a cone-shaped gear at the end. The output shafts are just simple gears. (Their teeth are cut as curved, not straight - this helps them interlock properly and cuts down on noise; straight-cut gears on old offroaders and such tend to produce a loud whine.)
Now, the cone works just like a set of gears, each smaller than the previous one. At the base of the cone, the gear ratio is high and the torque is low. At the tip of the cone, the gear ratio is low and the torque is high. While driving straight on a dry surface with good grip, the output gears sit at the same height on the cone. The gear ratio of the spin, transferred from the input shaft to the output shafts, is the same. Both wheels spin at the same speed.
When a car turns, the outside wheel spins more quickly, so its gear travels towards the base of the cone; the gear ratio gets taller, with the output gear making more revolutions per one cone revolution. The inside wheel travels away from the base of the cone, the gear ratio gets shorter, and its output gear makes less revolutions. Effectively this is the same as the outside wheel shifting up a gear and the inside wheel shifting down a gear. This is what happens when both wheels have the same amount of grip.
But the differential is primarily meant to transfer torque, and torque goes down the path of least resistance. The more grip the wheel has on the ground, the more resistance to spinning it feeds back to its gear - and the less grip it has, the less resistance it gives.
Now, here is the counter-intuitive bit that took me a while to figure out, pondering over a simple drawing of a diff. Resistance makes the gear away from the base of the cone, looking for a shorter gear ratio and less spin. In normal circumstances both wheels have more grip than torque, so when you feed the grip in, the wheels simply start turning and you go forward. But torque really just wants to make the wheel spin freely, so if one wheel has significantly less grip, it will be as if the other wheel is stuck. Its gear will move so far up the cone, looking for less revolutions and more torque to move it, that it will simply pop off the tip of the cone. On the other hand, the wheel with no grip will use less torque to start slipping and its gear will be happy at the base of the cone, spinning quickly but getting little torque.
So you see, torque does travel down the path of least resistance - but not because more torque can be used there, but because less torque is required there. Torque is lazy like that.
To combat this situation, where one wheel is spinning and the other is stationary, engineers use a limited-slip differential. It has a sort of bypass gearing setup, where a certain amount of torque from one output shaft is fed to the other. As long as they are both spinning at the same speed and getting the same amount of torque, it doesn't matter; but if one wheel pops off the tip of the cone and loses torque, it will still get some from other wheel. Limited-slip diffs are rated in percent, as in, how much difference in percent can there be between the amount of torque the wheels are getting.
Active differentials, like the ones on the Mitsubishi Evo or Subaru WRX STI, are limited-slip diffs that have electronics controlling the rate of torque transfer through the bypass.
Locking diffs are much simples. You push a button (or, much more satisfyingly, pull a lever) and the gears are simply held in place, not allowed to travel up and down the cone. Both wheels get half of the torque, but they can't move at different speeds, so turning is tricky. Useful for offroaders though.
And torque steer? Oh, quite simple. In a FWD car, for packaging reasons, the output shafts are different lengths (because the gearbox hooks up right to the differential, it usually can't be in the middle of the axle). Because it takes a bit of torque to spin the shaft itself, more if it's longer, one wheel will get more torque than the other. More torque on one side means that the car will pull in the opposite direction. Besides, differentials are made so that the torque actually travels to one side before the other - normally it makes no difference, but if there's a lot of torque to put down, it does; which is why very powerful RWD cars will throw the tail end to one side under hard acceleration.