Gary Satanovsky gives us a great 'nutshell' story behind the Day, from FamousDaily.com:
A new country needed a new flag to represent them. During the American Revolution, the first Continental Congress resolved to design the flag of the United States “thirteen alternate stripes red and white” representing the thirteen original colonies, and that “the Union be thirteen stars, white in a blue field, representing a new Constellation.” That design was based on the “Grand Union” flag bore by the Continental Army in 1776. With the design settled, it was time to adopt it.
On this day, June 14, 1777, the “Stars and Stripes”, the official National symbol of the United States of America was authorized by the Continental Congress. As recorded in their journal for that date, the item read: “Resolved that the flag of the thirteen United States be Thirteen stripes alternate red and white: that the union be thirteen stars, white in a blue field, representing a new constellation.”
According to legend, in 1776 George Washington commissioned Philadelphia seamstress Betsy Ross to create a flag for the new nation. Although she most likely knew Washington and did sew flags, better evidence suggests the creator was Francis Hopkinson, a delegate to the Continental Congress from New Jersey.