Muscles in your chest and abdomen contract, or tighten, to create space in your lungs for air to flow in. The muscles then relax, causing the space in the chest to get smaller and squeeze the air back out.
Inspiration (breathing in).
The diaphragm contracts and moves downwards. The intercostal muscles contract and move the ribs upwards and outwards. This increases the size of the chest and decreases the air pressure inside it which sucks air into the lungs.