What do the stars and stripes of the US flag represent?

The thirteen red and white stripes of the US flag represent the first thirteen American colonies.

The fifty white stars represent the fifty states of the United States of America.
The Flag Act of April 4, 1818 - provided for 13 stripes and one star for each state, to be added to the flag on the 4th of July following the admission of each new state, signed by President Monroe. The stripes effectively stand for the original 13 states while the stars represent all the current states.

The current flag is based on the Executive Order of President Eisenhower dated August 21, 1959 - which provided for the arrangement of the stars in nine rows of stars staggered horizontally and eleven rows of stars staggered vertically.