Your routine is what you do when you enter the batter’s box. It’s just something to get yourself ready both physically and mentally to hit. Many players will tap their shoes with the bat, take a couple swings of the bat or even tap the plate with the bat. After going through their routine they will establish a rhythm.
One sometimes overlooked aspect of hitting is rhythm. You might remember the late great hitting instructor Charlie Lau mentioning that tension is one of the main enemies of good hitting. You need to get rid of tension at the plate. One way that many hitters do this is through movement of some kind. Some hitters rock back and forth slightly while others might wiggle their hips or move their elbow around. This movement loosens and relaxes your body which makes your reaction time better and your swing more fluid. Obviously you don’t want to have too much movement and you don’t want to do anything that will cause you to not see the ball coming out of the pitchers hand. A simple rock back forward and back might work the best.
Recoil occurs as the pitch is being released from the pitchers hand. It’s the shift of weight more toward your back leg in preparation for swinging the bat. For many hitters this is a subtle movement while for others it is more exaggerated. Some hitters will even lift their front foot off the ground as they rock back.
Here is a great video that puts all these factors together and gives you a good idea of how to approach the plate…