Lockers:

What do Differential lockers do? Lockers mechanically "lock" the differential and force the axleshafts to spin at the same rate.

What does a differential do? Differentials split torque from the engine evenly between the two axleshafts, while allowing each to spin at different rates, this allows for the tires to spin independently when needed, such as when going around corners.

How does locking them help me? Differentials are complex things, and we'll link to extra reading at the bottom, but the basic idea is this: Imagine you have open differentials and one tire in the air. As the engine applies power to the differrential, it takes the path of least resistance and spins the wheel with least friction, in this case spinning the wheel in the air and leaving you stuck. Now, imagine the axleshafts were mechanically locked together, the power from the engine has no path of least resistance, and must rotate both tires at the same time, allowing you to drive away. That's what lockers do, when they are activated and power is applied, they ensure that both axleshafts always spin.

How much difference does this actually make? Having good lockers and knowing when to use them will get you through trails that Jeeps with open differentials couldn't hope to pass without spinning tires, it is one of the most helpful upgrades off-road for Jeeps.

Sounds great! Should I know anything else before I install one? Lockers aren't perfect, and can be somewhat tempermental on the road. If you're in slippery snow a lot, you might benefit more from a limited slip differential. Some axles are a bit weak to handle lockers too, the TJs stock Dana 35 axles can struggle to support the added stress from a locker, so you might have to upgrade your axle a bit beforehand or look into a limited slip diferential which will still help a lot off-road. It's important to research the different kinds of lockers before you decide what might be best for you

What different types of locker are there? There are two different types of common lockers: Selectable Lockers and Automatic Lockers. Limited Slip Differentials are also a common choice, and are kind of like a mid-point between open diffs and lockers.

Further Reading: How is torque delivered to the wheels on a 4x4?(external link)

If you're looking into Differential Lockers, it's a good time to consider Regearing Your Axles. The work needed for a Regear closely aligns with the work of installing a locker, so you can save some money by doing both at the same time.