Although today is referred to as “President’s Day” it is not a federal holiday by that name. It is officially designated as Washington’s Birthday under federal law. There was a movement to combine both Washington and Lincoln’s birthday (since they occur days apart) or honor the office of president. That never came to be. Instead in 1968 the Uniform Monday Holiday Act was past and came into force in 1971. That shifted most federal holidays to a Monday if it fell during the week. Washington’s Birthday name was not changed and so under federal law it is still Washington’s Birthday. However many states issue their own proclamations celebrating not only Washington but Lincoln and others from their own state. Advertisers have caught on as well. So today many call it President’s Day but who it commemorates beyond George Washington is up to the state governors.

The unity of Government, which constitutes you one people, is also now dear to you. It is justly so; for it is a main pillar in the edifice of your real independence, the support of your tranquility at home, your peace abroad; of your safety; of your prosperity; of that very Liberty, which you so highly prize.
President George Washington,Farewell Address, 19 September 1799.

For more information:

Britannica.com
George Washington’s Mount Vernon
History.com