Overlap is a basic animation concept. Essentially, overlap is what its definition implies: one action is overlapped or offset relative to another. This give the animation a sense of life or natural movement. A great real world example of overlap is frequently seen at music concerts, where everyone has their hands above their heads, and waving their arms back and forth. Typically you will see wrist movement either at the beginning or end of the arc of motion of the wave (sometimes both), while the lower arms and upper arms rotate at slightly different time ranges from each other. Had this not occured, the motion of the wave would be more akin to waving broomsticks. In this example, it is the overlap that imparts an arc shape to the wave.
Motion overlaps can occur between both in space and in time, or sometimes just one or the other. Its all up to the needs of the scene, of course. As you animate, you will find that arms, legs, head motion, spine motion, hair and so on will all look far more natural with overlapping motion and/or timing. Further, tails, tentacles, antennae, and costume acouterments like bangle bracelets, earrings, shoulder bags, and clothing are all great opportunities for overlapping motion.