If you get the virus, your body produces systemic and mucosal antibodies. When you get the vaccine your body produces systemic, but not mucosal antibodies. Breakthrough cases are people exposed to the virus. It attacks the respiratory(mucosal) system giving them a mild flu like experience. The systemic antibodies generally keep it from becoming worse. Thus a “break through” infection.
FYI-Fully vaccinated people with weakened immune systems are still at high risk.