Both Jose Altuve and Edgar Martinez have gone on record saying they consciously work on their ability to “scissor”, or in other words, have the back foot kick back behind them as their front leg braces and they get to and through contact with the baseball.
Reciprocal movement can be described in exactly this manner: one side of your body moves in one way while the other half of your body moves in the other way.
For example, in all 3 demo clips, we can see different variations of reciprocal movement in action, in a multitude of different sports: the slapshot, golf swing (albeit in the air), and the tennis return. Each of these movements demonstrate the principle of reciprocal movement.
As the “swing” gets accelerated forward, in each of these movements, we see the hips decelerate and create a stable foundation for the upper body to work against as it accelerates. The result? The lower half/upper half working in opposition of each other to produce increased efficiency and power.