First of all, yes, International Towel Day is a real thing.
International Towel Day is celebrated each May 25. It’s a memorial to author Douglas Adams (the increasingly mis-named Hitchhiker’s Guide to the Galaxy trilogy) As a tribute, some fans carry a towel with them to demonstrate their appreciation for the books and the author. The first Towel Day was two weeks after Adams’ death on May 11, 2001.
And a quote:
… a towel has immense psychological value. For some reason, if a strag (strag: nonhitchhiker) discovers that a hitchhiker has his towel with him, he will automatically assume that he is also in possession of a toothbrush, washcloth, soap, tin of biscuits, flask, compass, map, ball of string, gnat spray, wet-weather gear, space suit etc., etc. Furthermore, the strag will then happily lend the hitchhiker any of these or a dozen other items that the hitchhiker might accidentally have “lost”. What the strag will think is that any man who can hitch the length and breadth of the galaxy, rough it, slum it, struggle against terrible odds, win through, and still knows where his towel is, is clearly a man to be reckoned with.
— Douglas Adams, The Hitchiker’s Guide to the Galaxy, Chapter 3