The phrase “shot heard around the world” is a common expression that has occurred in a few historical events that means that it is the event that started the war or event. In the case of the American Revolutionary War, this phrase is used to explain the beginning of the Revolutionary War.
Even though there were events that took place prior to the war that were skirmishes or conflicts between the colonists and British soldiers, the actual first start of the war was at the beginning of the battles of Lexington and Concord.
When the first shots from the militia were fired at the North Bridge in Massachusetts, this caused the first British soldiers to die. Then the war began.