A nice example of Boyle's Law is a syringe. As you decrease the volume of the syringe, by pushing in the plunger, the pressure goes up, ejecting the liquid inside. Conversely, as you increase the volume by withdrawing the plunger, the pressure decreases so the higher pressure outside will drive liquid inside.

Balloons: Have you ever popped a balloon? If yes, then you've exploited Boyle's law. As you press on a balloon, the volume decreases, making the pressure increase. At a certain point, the material of the balloon can not withstand the pressure, so it pops.

Great question! It's nice to see that science works outside the classroom, isn't it?

Boyle's law describes the pressure-volume law of gas dynamics, that pressure times volume is a constant if temperature and mass do not change. It's what make pistons work in engines.