In the center of your axle there is a Differential (circled in green above). If you have Independent Suspension you still have a differential, only it is bolted to the vehicle in the center of the suspension assembly rather than being part of the axle. The differential contains the gears that convert the rotation of your driveshaft to rotation of the axle shafts, and the design of the differential determines how much of the power is transferred to each tire.
The reason a differential exists in the first place is that when you go around a corner the outside tire has to travel farther than the inside tire, so it has to spin faster. Without a differential dealing with this speed difference you would drag a tire on every corner.
There are four basic designs for a differential:
Open - This is your standard differential that has gears to allow the outside tire to move faster than the inside tire when cornering. It gives the best handling but power goes to the path of least resistance, so if a tire spins then the other tire on that axle gets no power.
Limited Slip - Gears or clutches ensure that each tire always gets small amount of power, even if the other is spinning. It may only be 10-20% of your engine power, but in all but the most challenging situations it should be enough to keep you moving. It can't compare to a true locker for traction, but it is much more street friendly.
Locker - Spring loaded teeth Keep the two sides of the axle locked together, so both tire spin the same speed. When cornering on the road the strain caused by the tires trying to travel different speeds makes the springs release and the locker ratchets to release the strain. Depending on the locker this can happen relatively smoothly, or with a jerk and a bang. Typically the more tough and durable lockers have the worst driving manners, and having the tires locked on slippery streets can make the back end of the vehicle very twitchy.
Switchable (Selectable) locker - The best of both worlds, a switchable locker is Open until you activate it. This allows for good street manners and lets you choose whether you want to try an obstacle without the help of the locker for more of a driving challenge, but is fully locked when needed. Selectable lockers are also a great choice for a front axle, as having the front axle locked can make turning very difficult.
You can also replace your differential with a Spool. A spool locks the axle all the time, with no ratcheting action and no way to turn it off. Generally these are only used for off-road only rigs, as the street manners are horrible and the constant dragging of tires on corners wears them out fast.
What happens when your Open-Dif rig lifts two opposite tires
The final piece of information you need about adding lockers to you rig is that being able to keep putting power to the one tire that has traction can put a lot of strain on the axle, especially if a tire spins then suddenly regains grip. Put oversized tires and a locker in a light duty axle and you have a recipe for snapped axle shafts.