How does a ball get pumped up by the sun if it is left outside?

If a soccer ball that is otherwise able to hold its pressure fairly well is heated by the sun, it will, indeed, increase its pressure. Thermal energy is transferred to the air (which is already compressed) inside the ball, and it causes the gas atoms and molecules to increase their thermal energy. This thermal energy causes increased vibration and increased "bouncing around" among the heated gas particles. The increased kinetic energy added to the air by the heat of the sun has increased the pressure in the ball.