Inspiration: The first stage of inspiration is contraction of the diaphragm, which causes it to move downwards, and contraction of the external intercostal muslces (the muscles between the ribs), which causes them to move upwards and outwards. This movement increases the volume in the chest cavity, which therefore decreases the pressure in the chest cavity. The pressure decreases below the atmospheric pressure outside of the body. This pressure gradient causes air to rush into the lungs via the mouth from the outside (inspiration).
Expiration: Expiration is the opposite of inspiration, and causes air to leave the lungs. The first stage of expiration is relaxationof the diaphragm, which causes it to move upwards, and relaxation of the external intercostal muslces (the muscles between the ribs), which causes them to move downwards and inwards. This movement decreases the volume in the chest cavity, which therefore increases the pressure in the chest cavity. The pressure increases above the atmospheric pressure outside of the body. This pressure gradient causes air to rush out of the lungs via the mouth (expiration).