Do you mean a "We Love the [Title of Ruler]" day?
I don't know off the top of my head, but the happiness of the citizens of a city has something to do with these happening.
Anyway, depending on your system of government, one of the following can happend:
Anarchy: Nothing happends, but for a city to go into anarchy, there can't be many happy people anyway.
Despotism: When a city under despotism celebrates, the people collect resources as if the city was run under a monarchy.
Monarchy/Communism/Fundumentalism: When a city under these governments celebrates, it's people collect resources as if the city was run under a Republic.
Republic/Democracy: When a city under one of these governments celebrate, then for each turn it celebrates, the population roster grows by ONE, depending on whether theres enough food.
Hope this cleared things up for you.