Originally taking place on August 6th (the creator's birthday), Bowser Day was moved to August 4th because World 8-4 is the first true physical appearance of the King of Koopas in the original Super Mario Bros..
Similar to Super Mario Day (Mar. 10th), fans of the Super Mario series, and specifically the character Bowser, celebrate by sharing their favorite depictions, memories, and experiences with the aforementioned character. They also tend to produce a bunch of fan material, art especially and even writing, dedicated to the character.
Or making the wiki page on Bowser Day.
Oh, and a sudden spike in Rule 34 focusing on Bowser suddenly appears for some reason.
What ever could it be?