'Festive comedy' was sub-genre which a critic called Barber established with her book 'Shakespeare's Festive Comedy'. It argues that the spirit of the festival (meaning simply a public or religious holiday) was to turn the normal hierarchies of the social sphere upside down - and that unacceptable behaviour became acceptable for a single day.
We might see in Twelfth Night many thematic clues towards festive comedy: a play in which the main character is a woman dressed as a man, a play which is catalysed by a storm (literally turning everything topsy-turvy), and a play in which normal behaviour is subverted: Olivia comes out of mourning to woo Cesario, and Malvolio (usually unsmiling and severe) wears yellow stockings and smiles to woo Olivia.
Also associated with festive comedies are celebratory drinking and eating ('festive' is a close verbal relation of 'feast') and, when Toby turns on Malvolio, telling him that the 'cakes and ale' will stop simply because he is virtuous, many critics have argued that Toby and Malvolio represent respectively the festive and the puritan. Malvolio is compared to a puritan by Maria: and the puritans, against enjoyment of most kinds and certainly opposed to festive celebrations, were the enemy of having a good time!
In brief then: what are the main points that might make Twelfth Night a festive comedy? Turning social structure on its head, unusual behaviour, and cakes and ale.