When you throw a PokéBall at a Pokémon to catch Pokémon Go, you can increase your chances of catching it based on how well you throw. The white circle around the Pokémon determines the quality of your shot, and the one inside it that constantly shrinks determines the accuracy. If you throw your PokéBall inside the shrinking circle, you can receive a Nice, Great, or Excellent roll. Of the three, the excellent shot is the most difficult to achieve.
To get an excellent shot, you have to wait for the narrowing circle to almost reach the dead center of the larger circle. It creates a small icon in the center of the Pokémon, making it rather difficult to strike dead. You can only get an excellent shot by landing your PokéBall toss in the smaller circle, not waiting for the smaller circle to appear and then attempting to catch the Pokémon.
An initial strategy by some Pokémon Go trainers were to wait for the circle to become extremely small, then take their finger off the PokéBall. Unfortunately, you can't do this anymore and it resets it.
When the icon gets small enough, you throw your PokéBall on the one in front of you and hope it hits the icon. You'll know if it hit the smaller one because it will have a notification and tell you if it was a nice, big, or excellent shot. You'll likely switch between whether it's a Great or Excellent roll, especially when you try to wait for it to shrink.
A great way to rack up excellent shots is to do it on more common Pokémon, such as those you encounter while walking or hanging new PokéStops. It is much more exciting than it happens against legendary Pokémon and encounters with research activities. When you get the Excellent roll, the chances of you catching that Pokémon increase.
It takes some practice to nail an excellent shot. Due to how small the inner icon must be, it won't be easy and you probably won't want to try when the target Pokémon is far away. Try to wait until you encounter a Pokémon that is close enough to you.