There are a lot of versions of the idea where Presidents' Day comes from. It is a united day to honor all the presidents of the United States of America. 

Some people think that this is the observation of George Washington's Birthday. There is another point of view that this celebration of the combined birthdays of Abraham Lincoln and George Washington that used to be two separate holidays. Yet, there is an opinion that we honor the memory of all the presidents of the United States. So, which of these are true?  

The birthday of President George Washington, February 22, was celebrated in a very patriotic manner almost as Independence Day. Of course, the birthday of Washington became an official holiday in 1885. 
George Washington was the most important figure of the history of the United States and earned an honorary name – “the Father of the Country.” He was the commander of the Continental Army, the leader of the American colonies in the Revolutionary War, and the first President of the U.S.  

In the 1950’s, the idea to combine Lincoln and Washington's birthdays appeared. It should be noted that NATO proposed to combine the two dates into President's Day and made it a federal holiday in the United States. In 1971, the federal holiday of Washington's Birthday was shifted to the third Monday of February. President Nixon once said the following day was the one to honor all presidents of America. So, answering the initial question, President’s Day in the U.S., celebrated each third Monday of February, is all of the three, a day close to Washington’s birthday, later combined into one holiday with Lincoln’s birthday and is literally celebrated as the day to honor all the presidents of America.