Actually, tradition calls for us to fold the flag into the shape of a tri-cornered hat, the kind worn by George Washington and other soldiers who served in the Continental Army during the Revolutionary War. While the troops carried a variety of flags during that war, the tradition of folding the flag in the manner we do today is specific to the Francis Hopkinson and Betsy Ross versions (and their decedents) of our national colors.
The flag is folded and tucked so that it has a similar appearance to that of a cocked hat, reminding us of the soldiers who served under General George Washington and the sailors, the Marines who served under Captain John Paul Jones. Some people also interpret it to represent the three branches of government (Executive, Legislative, and Judicial) under the US Constitution.
The flag was not always folded as we do today. In fact, best sources trace the current practice not to the time of the Revolution but to the early 1950’s when the Gold Star Mothers of America and an Air Force chaplain stationed at the United States Air Force Academy developed the procedure complete with a meaning for each fold. Regardless of its source of origin, it is provided as a patriotic service to all.