A hesitation stroke is kind of a "feel" shot. You give it a one-pump and then a two-pump. It reassures a much finer stroke from the cueball to the object ball.
I usually grip my cue in the middle of the butt and then I'll slip stroke it a little with a one-pump and a two-pump, and then my hand will gradually go back a little bit further on the two-pump. It's a little bit of a slip stroke.
It takes a lot of experimenting with this technique, but if you practice, you will gradually become comfortable with it. The balls will go a lot smoother in the pockets, and you'll feel the authority that is needed with better precision from the cueball to the object ball to the pocket.
Experimenting with the different englishes, bottom right, inside left, center, kill, et cetera, will help you recognize the correct finesse to apply to the shot. On the force follow medium right english, for example, aim your cuestick a little bit downward with the butt end a little bit more up in the air.
When I started understanding the hesitation stroke, I didn't actually get it at first, but as I worked on it and developed all the different angle shots involved, I started using it on almost all my shots. It made the shots a lot easier. I could put the cueball on automatic pilot without thinking about it. I could play the cueball in like a 6-to-8-inch vicinity and get it there every time, no matter where I was at on the table. If it was going 2 rails to get shape, 3 rails to get shape, I got there. Very seldom I would get snookered because I knew exactly where the cueball was going.
The hesitation stroke did make me a better player than I was at the time. My cueball control went up to a speed that was like the 8 and 9 better than my original speed in just a short time.