In simpler terms, inside your mechbox there is a cylinder and a piston. The piston gets pushed into the cylinder and compresses the air which comes out of the nozzle to propel the BB. Think of a syringe.
A bore up cylinder is one with thinner walls but more interior area so there is more air inside. Matched with a bore up piston head, the air volume compressed is greater.
Cylinder ports are holes in the side of the cylinder that allow air to escape for correct cycling with shorter barrels. If you have a really long barrel, an unported cylinder doesn't allow the air to escape during a stroke and gives the bb more pressure to properly make it's way down the longer barrel.
Kit for M16: