The humorous phrase in one’s birthday suit means: in a state of nudity.

In this phrase, which refers to the naked condition in which a person is born, the noun birthday has the sense, now rare, of the day on which a person was born.

The noun birthday occurs in this rare sense, for example, in Surviving the First Few Months, the first chapter of Parenting: The Missing Pages (Xlibris Corporation, 2011), by Leslie LB Cruz [page 13]:

Your parenting journey is in full swing on your baby’s birthday. The road toward raising your baby may seem long and slow at this moment, but day by day, week by week, you will witness how quickly your baby grows physically and mentally.

Variants of the phrase in one’s birthday suit include in one’s birthday clothes, in one’s birthday gear and in one’s birthday attire. The variant in one’s birthday attire occurred, for example, in the following passage from A Tour throughout South Wales and Monmouthshire (London: Printed by J. Nichols and Son, 1803), by the British author John Thomas Barber (1774-1841) [page 26]:

As we were strolling on the sands, about a mile above the town, we remarked a group of figures, in birth-day attire, gamboling in the water: not suspecting that they were women, we passed carelessly on; but how great was our surprize, on approaching them, to find that the fact did not admit of a doubt. We had not paused a minute, before they all came running toward us, with a menacing tone and countenance, that would seem to order us away.

Note: The noun birthday suit was also used in the sense of a suit worn to celebrate the anniversary of the day the British sovereign was born. This is illustrated by the following passage from A New Tale of an Old Tub: Or, The Way to Fame. An Odd Sort of a Story (London: Printed for M. Cooper, 1752) [page 3]:

I have known a Gentleman make the Tour of all the Courts of Europe, to collect Hints for a Birth-day Suit, to out-do all at home on a Royal Birth-day.

The earliest occurrences that I have found of the phrase in one’s birthday suit and variants are as follows, in chronological order:

1-: From Manuscripts of the Earl of Egmont. Diary of Viscount Percival Afterwards First Earl of Egmont (London: Published by His Majesty’s Stationery Office, 1920), by John Perceval (1683-1748), 1^st Earl of Egmont [Vol. 1, page 279]—the following, dated Friday 2^nd June 1732, is about Mr. Spencer, younger brother to the Earl of Sunderland:

It seems this young gentleman is fond of frequently bathing, and has a bath in his house. By mistake a gentleman who came to see him was admitted while he was in the tub, whereupon making a short visit, he took his leave that he might not keep Mr. Spencer too long in the water; but Mr. Spencer out of a sprightly and frolicsome humour, leaped out of the bath, naked as he was, and waited on him down to the very street door. The Queen at her levée, talking of this action as a very extraordinary one, my Lord Peterborough replied that Mr. Spencer was a man of extraordinary breeding to acknowledge the favour of a common visit in his birthday clothes.

2-: From Strephon and Chloe, in A Beautiful Young Nymph Going to Bed. Written for the Honour of the Fair Sex (Dublin printed: London reprinted for J. Roberts, 1734), by the Irish satirist, poet and Anglican cleric Jonathan Swift (1667-1745) [page 20]:

To see some radiant Nymph appear
In all her glitt’ring Birth-day Gear,
You think some Goddess from the Sky
Descended, ready cut and dry.

3-: From England’s Genius: Or, Wit Triumphant. Being a Collection of Several Hundred Elegant, Satyrical Jests, and Witticisms, Sharp Repartees, Brilliant Thoughts, Merry Poems, and Admirable Sayings, of the Most Celebrated Wits and Punsters of the present Age. Taken from the Politest Conversations, as Drawing-Rooms, Assemblies, Balls, and the Bar. Also from the Bedford-Head, Key and Garter, and Rump-Stake Clubs. And the other Genteel Resorts of the Beau-Monde (London: Printed for J. Roberts, 1734) [page 3]:

A grave Noble Peer made a Visit one Morning to a gay young Gentleman of Quality, who received him sitting in an Elbow Chair, quite naked: There were loud Complaints made in the Town of the Indecency of the Action, besides the Disrespect shewn to a Person of such high Quality: The young Gallant said, That he thought he had paid his Lordship the greatest Compliment, by receiving him in his Birth-Day Suit.

4-: From The Genuine Sequel to the Essay on Spirit (Dublin, Printed: London, Reprinted for R. Baldwin, 1752), by the Irish Protestant bishop Robert Clayton (1695-1758) [page 58]:

I must own, such Antagonists as the Rector of Gaulkshill, and two or three paltry Scribblers, who have appeared against me, are enough to provoke a Man to Perseverance in Error, by the frightful Appearance in which they dress up Truth, which had better come abroad in her Birth-Day Suit, than be cloathed by them in such unbecoming Garb.

5-: From The Adventures of Ferdinand Count Fathom (London: Printed for W. Johnston, 1753), by the Scottish novelist Tobias Smollett (1721-1771) [Vol. 2, page 43]:

This morceau being sealed and directed, was forthwith carried by our adventurer to the lodgings of the major, who had by this time, retired to rest, but hearing the count’s voice, he got up and opened the door in cuerpo, to the astonishment of Ferdinand, who had never before seen such an Herculean figure. He made an apology for receiving the count in his birth-day suit, to which, he said, he was reduced by the heat of his constitution, though he might have aligned a more adequate cause, by owning that his shirt was in the hands of his washerwoman; then shrouding himself in a blanket, desired to know what had procured him the honour of such an extraordinary visit.

6-: From The Spectacles, a tale set in a nunnery, in The Muse in Good Humour: Or, A Collection of Comic Tales (London: Printed for Francis Noble and John Noble, 1757) [Vol. II, page 66]:

A Man there must be in Disguise,
The which he wore to ’scape Surprize;
Therefore at once the Truth to have,
She [i.e., the Abbess] to the Nuns this Order gave;
“Strip every Maid to find this Dragon,
“Let not a Sister have a Rag on.”
[…]
To full View, each lov’ly Maid,
Stood in her Birth-day Suit array’d,
With beauteous Shape and graceful Mien.