There are three parts or steps to cueing and delivery of the cue.
Step one,
The feathering of the cue ball. Is the action when the player (in the cueing position) begins to move the cue back and forth preparing to strike the cue ball? The feathers or feathering the cue ball is to relax the cue arm preparing to play the shot. This is also a good time that the player can tell himself/herself, whether they have done all their pre-processes correctly and believe they are on-line to play the shot.
Step two,
Pulling or drawing the cue back. Pausing before drawing the cue back allows the player to divide the feathers from the draw back. Drawing the cue back should be totally controlled. This is done by keeping a straight cue on the draw back. Controlling the draw back prepares the player to control the cue, ready for delivering the cue.
Step three,
Delivering the cue, again implementing a pause. Divides the controlled draw back, from the delivery of the cue.
(The pause also reduces cue recoil. Cue recoil is when a player delivers their cue, only to pull the cue back in the same action (like jabbing the cue). Cue recoil can cause the habit of cue deceleration. Cue deceleration can cause many errors to your play, such as losing cue ball control which loses position and also sending the cue ball in a slightly different direction than the desired direction).
Pausing before delivering the cue can help the player to learn how to deliver the cue forward only. Delivering the cue is, and should be totally controlled keeping the cue straight throughout this action and going through the cue ball regardless of where the player is hitting the cue ball.