Shakespeare scholars believe that Twelfth Night, or What You Will was commissioned by Queen Elizabeth I as part of the Twelfth Night celebration held at Whitehall Palace on January 6, 1602. The occasion of the celebration was the end of the diplomatic service to Elizabeth's court of Don Virginio Orsino, Duke of Bracciano.

Perhaps Shakespeare hoped to honor or flatter the Duke by naming the character of Orsino after him. Hopefully, the real Duke Orsino had a good sense of humor about being portrayed as the impulsive, lovelorn Orsino in Shakespeare's play.

The title of the play might have been inspired by the occasion for which it was written, that of Twelfth Night, which might have inspired Shakespeare to write a play that reflected the title of the play as well as the occasion.

Aside from the Twelfth-Night traditions of women dressing as men, role-playing, and the general upsetting of societal norms, there's no reference in the play to Twelfth Night, Epiphany, or anything related to Christmas, although the subtitle, What You Will, is entirely appropriate to the play.

Shakespeare seems to have taken advantage of the opportunity to bravely and boldly satirize some individuals in Elizabeth's court, which was something Shakespeare might do with impunity only at Twelfth Night, when servants could be masters and the rules of social order and decorum were suspended for the occasion.

It's believed that Shakespeare's Olivia represented the Queen herself, who could be fun and even flirtatious but was undeniably brave and steadfast as well.

The character of Malvolio is thought to be a caricature of Sir Christopher Hatton, Elizabeth’s steward. Sir Christopher was meek, toadying, and submissive to Elizabeth (and at one time, he apparently attempted to woo her) but mean-spirited and overbearing to Elizabeth's servants and courtiers, who found him foolish and ridiculous and mocked him behind his back.

As for the business of Malvolio's famous yellow stockings and cross-gartering, Lacey Baldwin Smith writes in Henry VIII, The Mask of Royalty that when Henry VIII received news of the death of his first wife, Catherine of Aragon, he "celebrated with a masque, banquet and ball where Henry, cross-gartered in yellow hose, danced the night away with Anne Boleyn.”

Shakespeare might have been able to claim deniability for any correlation between Elizabeth's court and the characters in Twelfth Night by setting the play in far-off Illyria, in the Balkan Peninsula, across the Adriatic Sea from Italy in what is present-day Croatia, Bosnia and Herzegovina, and Albania.

The title, Twelfth Night, likely represents Elizabeth's commission and the occasion for the play's performance, and the subtitle, What You Will, reflects the content and tone of the play itself and Shakespeare's apparent carefree abandon in writing it.

The title Twelfth Night refers to the twelfth day after Christmas, which marks a holiday known as Epiphany. Epiphany celebrates the arrival of the Magi, or Three Wise Men, to deliver their gifts to baby Jesus. While one might expect an Epiphany celebration to be much like the rest of Christmas festivities, apparently in Shakespeare's day the celebrations were known to be quite wild. Shakespeare in particular wrote the play in 1602 for a festivity held at one of the Inns of Court, and that particular festivity was known to be "absolutely secular and even quite bawdy," meaning having absolutely nothing to do with religion and even very obscene ("Shakespeare's Twelfth Night"). Epiphany celebrations were also known to be "a time of masques, revels, defiance of authority, and general foolishness" ("Shakespeare's Twelfth Night"). Epiphany has also been described as a "time when excess and license were expected to run rampant ... a time of merry-making, of hard drinking, and of romantic (or lusty) pursuits" (eNotes, "Twelfth Night: Themes"). We can see exactly how Shakespeare's play portrays all of the above descriptions of Epiphany, making Twelfth Night, especially the play's subtitle, Or What You Will, the perfect title for the play written for an Epiphany party.

The play's secular and bawdy themes are mostly portrayed through the antics of Maria, Sirs Toby and Andrew, and Fabian. In particular, their treatment of Malvolio can be seen as bawdy, or obscene, meaning "offensive to morality or decency" (Random House Dictionary). While Maria's letter tricking Malvolio into believing Olivia is in love with him may have been amusing, capturing the merriness of Epiphany, Sir Toby crosses the line when he decides to have Malvolio locked up in total darkness as a madman. Locking him in complete darkness can of course be seen as a form of torture and is quite cruel. The hard drinking characteristic of the night is also seen in Sir Toby's behavior, especially the drinking revelry he and Sir Andrew have late one night in the house in Act 2, Scene 3.  

In addition, the masquerading that is a frequent part of an Epiphany celebration is of course captured in Viola's plan to disguise herself as a boy, which also runs contrary to social norms, capturing theme of "defiance of authority." Finally, we also have the love triangles in the play, which capture the theme of romance or lust.