The beaker production in fundamentalist cities is cut in half. If the science rate is set above 50%, it still counts as 50% in beaker production. And after doing a little experiment, it turns out the beakers aren't wasted, but counts as gold. I.e. the additinal percentages over 50% are added to the Tax-percentage. So, in fundy a 30/50/20 rate is equal to a 10/70/20 rate. Sorry for saying the wrong thing.
Celebration is when they celebrate We Love the _ Day. Whenever a city does this it will receive some advantages.
Despotism:
It gets the same production as a city in Monarchy, Communism or Fundamentalism. I.e. normal productivity, the one it says in the Civilopedia.
Monarchy, Communism or Fundamentalism:
It gets the same production as a city in Republic or Democracy. I.e. one more trade on each square already producing a trade arrow.
Republic or Democracy:
The city will grow an entire pop from the turn after it starts celebrating, as long as there is enough food and the required improvements are built (Aque and Sewer).
This means that a celebrating fundamentalist city will produce an extra trade arrow, just like in democracy and republic. So, by celebrating, the fundamentalist cities can produce the same huge amounts of trade arrows as a repbulic or democratic city, and therefore give as huge pay-offs when freights are delivered.