Is it “Presidents” Day or “Presidents'” Day?
It’s both. The holiday actually celebrates the lives of George Washington and Abraham Lincoln, the 1st and the 16th president of the US, respectively. Washington’s birthday is February 22. Lincoln’s birthday is February 12.
Because the holiday celebrates two presidents, Presidents’ Day (with an s and an apostrophe) is correct. The Gregg Reference Manual recommends that version.
The Associated Press Stylebook, uses Presidents Day–with no apostrophe. Most of the catalogs and newspaper advertisements featuring sales on that day are using the AP version.
How can the AP version be correct? Because sometimes we use a word as an adjective–not a possessive form. For example, many people can name a Beatles song–not a Beatles’ song.
For more about possessive forms, read this post.