How can a vaccine prevent an infectious disease

Vaccines reduce the risk of infection by working with the body's natural defenses to help it safely develop immunity to disease. 

The vaccine technically puts the illness directly inside of you, but its a very minor version. Your body will create white blood cells that fight off the illness, and that will make them (the white blood cells) stronger. So by the time lets say for example, the flu reaches your body, you'll already have strong white blood cells to fight off the illness.