That all depends what you really mean by the question....
The easy answer is that they are all the ones the CO expects you to attend and for which the PMC on his behalf issues a 3 Line Whip. These are normally Guest Nights, the Summer Ball and one or 2 Ladies' Nights. The frequency varies a lot, depending on the Mess about in Regimental Messes, perhaps once a month. In non-regimental Messes it varies even more depending on who runs the Mess and where you are, some are socially busy, others almost dead!
An alternative answer is that the official functions are the ones laid down in the Mess contract and for which staffing etc is found from within that contract.
In BFG, each mess is granted 10,000 euros to use on Official Functions (that is to pay for staff (until 0000hrs), food, and any related costs (not to include alcohol), not sure on UK messes.
As long as a function is Official then you can use this money to offset the function costs spiralling out of control. Official functions in a Regtl' mess would amount to 1 every three months with the odd BBQ, afternoon etc, but as already mentioned, depends on individual messes.