June 21 is always the 172nd day of the year, unless it's a leap year in which it is the 173rd day of the year. This is on a Gregorian calendar, which leaves 193 days remaining until January 1st, where a new year beings. June 21 marks the summer solstice in the northern hemisphere and the winter solstice in the southern hemisphere. That means that June 21 is typically the day of the year year with the longest hours of daylight in the northern hemisphere and the shortest in the southern hemisphere.
You can tell already that June 21 is an important date to mark for several reasons. Here are several events that have happened on June 21 in the past:

524 - Burgundy triumphs over the French in the Battle of Vezerone

1749 - Halifax, Nova Scotia, Canada is founded.

1788 - New Hampshire ratifies the Constitution and as a result is admitted as the 9th state in the United States.

1798 - The British Army defeats Irish rebels at Battle of Vinegar Hill in the Irish Rebellion of 1798

1813 - Laura Secord(the person not the chocolate) sets out to warn British forces of an upcoming attack on Queenston, Ontario by the U.S.

1826 - In the Battle of Vergas Maniots defeat Egyptians under Ibrahim Pasha

1864 - The Tauranga Campaign ends.

1887 - Queen Victoria's golden jubilee.

1898 - Guam becomes a U.S. territory.

1919 - During the Winnipeg General Strike, Royal Canadian Mounted Police fire a volley into a crowd of unemployed war veterans that kills two people

1945 - Battle of Okinawa ends in WWII.

1965 - Folk rock band The Byrds release their highly influential debut album Mr. Tambourine Man.

1982 - John Hinckley is found not guilty by reason of insanity for the attempted assassination of U.S. President Ronald Reagan.

1989 - The U.S. Supreme Court rules in Texas v. Johnson that flag burning is protected speech under the United States Constitution.

2000 - Section 28 repealed in Scotland with a 99 to 17 vote.

2003 - J.K. Rowling's fifth book in massive series of Harry Potter, "Order of the Phoenix" is published

2004 - SpaceShipOne launches and quickly becomes the first privately funded spaceplane to achieve spaceflight.