the first thing that happens when you breathe in is your rib cage rises and expands out. this gives your lungs room to inflate. then your diaphragm pulls down, causing air to rush from a high concentration into your lungs. (low concentration) as the air is sucked in your lungs inflate
Your lungs themselves do not inflate/deflate. The diaphragm and intercostal muscles contract and expand the chest cavity. This expansion lowers the pressure in the chest cavity below the outside air pressure causing air to flow in through the airways and inflate the lungs.