Vampire legends have been around long before Bram Stoker published his book, and can be found in many cultures from Europe to Asia. So has the belief that garlic can ward off evil spirits. 

The healing properties of garlic have been noticed in almost every country where it grows. It has been used as a natural medicine for hundreds of years. In medieval times, people believed that diseases were caused by bad air, and since using garlic could cure (and prevent) disease the people began to think that it had some sort of purification properties. People used to hang garlic in their homes to keep away bad air, and this lead to a superstition that garlic was effective against evil spirits. This is the source of the belief that garlic could keep vampires away.