So, despite my request, someone asked me to explain Hag Days. I'm going to try, but I think it's possible that Hag Days might actually be inexplicable.
Hag Days was an annual event in Bear Lake, and it was a strange town festival, the sort of thing you might have expected to see in Stars Hollow, except so totally politically incorrect that it couldn't possibly have happened in Stars Hollow.
The core of Hag Days was a competition amongst teams. They all wore funny costumes, and one particular person per team would be 'The Hag' -- dressed in the funniest, ugliest, batty old lady costume. Teams would participate in a variety of vaguely embarrassing, quasi-sexual, semi-athletic events and at the end of the day, one of the teams would win. For certain values of win that include 'managed to humiliate themselves faster and better than all the other teams'.
For non-competing people, there'd often be a children's fun fair, a potluck dinner or a pancake breakfast, and the general joy of watching people humiliate themselves in public. It was like a Japanese game show crossed with a Fourth of July picnic.