More air inside a basketball will make it bounce higher. The additional air hardens the leather or composite shell of the ball, making it more buoyant.
When a basketball has less air, the ball will not bounce as high. The shell of the ball is softer and compresses as contact occurs with another surface. A flat basketball is similar to a beach ball tossed around with less air. When the air in a basketball is increased the ball springs off the surface when contact is made.
Players used a soccer ball for the first game of basketball, and bouncing was not required in the original version of the game.