When the lever is set at Disengage the differential in the rear axle does its normal function. That is it lets one wheel turn faster than the other so that you can make tight turns without binding or dragging one wheel. (In a turn the outer wheel must travel farther than the inner wheel, so it has to turn faster).
When you Engage the differential lock lever it slides a set of dogs together and locks the differential. This causes both wheels to turn together. This is useful when you are going straight forward and one wheel begins to slip (spin). This is caused by more traction on one side than the other. The down side of a differential is that once one wheel starts to spin, there is virtually no force applied to the non-spinning wheel. By locking the differential you cause both wheels to have force applied to them. That way the wheel that still has traction can pull you out of your situation. Once you are in a place where both wheels have traction again, you want to dis-engage the lock.
Don’t use the lock while turning, especially if both wheels have good traction, it can cause things to break inside the axle.
Clear as mud?