People put their hand over their chest as it is part of a tradition. It is also part of the United States Flag Code, which goes into depth on how people should act when a pledge is being made.
It is a way of showing respect, and it is also a fact that when a hand is held over our heart, we are more honest in that moment. Pledging allegiance to the flag simply means you are showing that you are loyal to the United States of America, and forgoing a pre-existing citizenship. =)