Understanding pool billiards geometry will go a long way towards improving your game. Why a billiards ball moves in a specific direction upon impact is explained by using geometry. In order to get the most out of your shot, you need to know where the cue ball will go, what it will do to the impact ball, and where you will leave the cue ball for your next shot. All of this is explained by geometry.
Some of the specifics of pool billiards geometry are explained by understanding the angles. One rule is that the angle at which the ball hits the rail is equal to the angle it will leave the rail. Understanding this will help you with both bank shots and kick shots.
A pool table can be divided into diamond shapes, which help the players understand the geometry involved. The diametrical systems of billiards are a constant that players can use with the understanding of exactly where their ball will go when bounced off the rail. While there are geometric principles at play, the best way to understand this is to visualize the diamonds on the table. Pool tables often have marks on the top of the rail to help players find those diamonds and use them to their advantage.
When the cue ball hits the target ball straight on, it will continue in that straight line. However, you may need the target ball to move at an angle, which requires a cut shot. A cut shot is when the cue ball hits the target ball off-center allowing the target ball to travel at an angle.
Because of the connection between billiards and math, many analytical people enjoy the game. While having a simple understanding of the mathematical principles could help you understand the game, it is practice that will help put those principles into action.