It was an event held at schools. It was different with each school. Not all schools held field days. I am not sure if they still exist.
My school had pie eating contests, a visiting football team, water balloon fights, face painting, balloon animals, sack races and firefighters that brought a firetruck and sprayed water up in the air and the kids played in the spray as it fell. There were prizes and things to earn like extra school supplies and credits for the school bookfairs. My school held it in the summer.
Eating something potato related. It has to be real potato though. Mashed potatoes or baked potatoes seem to make me pretty sleepy.