Presidents Day (which is actually the federal holiday known as "Washington's Birthday," but is usually called "Presidents' Day" or "Presidents Day") is another one of our holidays that has evolved over the years. The third Monday in February, Presidents Day originally marked the birthday of our first President, George Washington. It has since come to represent, for many states, a conglomeration of both George Washington and Abraham Lincoln's birthdays (both of whom were born in February), George Washington and Thomas Jefferson's birthdays, or "U.S. Presidents" in general.
The holiday is furthered complicated by the fact (thanks, Wikipedia!) that the United States marks presidential birthdays by the Gregorian calendar, even though some of our presidents were born under (and lived during) a time period when "the colonies" and the newly-formed United States of America were actually still using the Julian calendar (introduced by Julius Caesar). The Gregorian/Western/Christian calendar is a solar calendar that fixes Easter closer to the time period of the year in which the holiday occurred when implemented by early Christians (Christians had previously used a lunar cycle, and the date for Easter had a lot more drift during the 19-year Julian cycle, if I am summarizing this correctly. See the related Wikipedia articles, or visit your local library, for more information).
President's Day is also treated by many as a holiday honoring veterans. George Washington is frequently referred to as the "Founding Father of our Country," and a "unanimously-elected president." But he was also a military general. He is credited with creating a medal of merit for common soldiers, and it is his face that is featured on the Purple Heart medal which is awarded to soldiers injured in battle.
Washington and Lincoln's birthdays used to be separately marked as federal holidays. These days, dependent on the state, many people do not have to go to work or school on the third Monday in February that is known variously as "President's Day," "Presidents' Day," or "Presidents Day," while some students get the entire week between Washington and Lincoln's birthdays as a mini-vacation from school. For many of us, the day also represents one of our multiple long weekends marked by outdoor barbecues with friends and family, and heavily-marketed blowout sales. Political figures give speeches, and it is up to us to individually decide what the holiday means in terms of our community and civic identity.