Together with expressions such as the fair(er) sex, the gentle(r) sex, the soft(er) sex and the weak(er) sex, the second sex denotes women collectively, regarded as inferior to men.

This expression was used by Howard Madison Parshley (1884-1953) as the title of the translation, published in 1953 by Jonathan Cape Ltd, London, of Le Deuxième Sexe, the title of an essay by the French philosopher Simone de Beauvoir (1908-1986), published in 1949 by Gallimard, Paris.

However, the expression the second sex had been used earlier in a philosophical context by Thomas Bailey Saunders (1860-1928) in On Women, published in Studies in Pessimism: A Series of Essays (London: Swan Sonnenschein & Co., 1891), translated from the German of Arthur Schopenhauer (1788-1860):

They [i.e., women] form the sexus sequior—the second sex, inferior in every respect to the first.

Note: The Latin adjective sĕcus means following in rank or order, i.e., less than something mentioned before, and its comparative, sĕquĭor, means lower, inferior, worse.
Interestingly, in The Metamorphoses, Lucius Apuleius, a Roman philosopher and satirist of the 2^nd century A.D., used the expression sexus sequior about a man disguising himself as a woman:

in sequiorem sexum incertus atque absconditus
     translation:
disguised and under cover of the lower sex.

The earliest occurrences of the expression the second sex that I have found are as follows, in chronological order:

1-: From Canto IV, in Don Juan. Cantos III, IV, and V (London: Printed for J. Onwhyn, 1821), by the English poet George Gordon Byron (1788-1824):

Oh! ye, who make the fortunes of all books!
Benign ceruleans of the second sex!
Who advertise new poems by your looks,
Your “imprimatur” will ye not annex?

2, 3, 4 & 5-: From The Satirist; or, the Censor of the Times (London, England):

2-: Of Sunday 18^th March 1832:

A good Joke.—At a ball the other evening old Talleyrand, treading in the path of being always seated on the crown of his breeches, and captivating all around him by that confounded wit of his, said to Lady Lyndhurst, “Have you heard the alarming news?” To which her Ladyship answered in the negative, holding up her hand, more to add strength to her negation than to show the beauty of her fingers. The episcopal diplomatist continued, “Dear Lady Lyndhurst, I am sure you will be shocked when I tell you that a Bishop was shot last night.”—“Gracious Heaven!” cried her Ladyship, stretching forth her arm, more in horror than display, “a Bishop shot! by whom, pray?”—“By several persons—all unknown!” Here the glorious old quiz was interrupted by Palmerston, who wished to say a word to him about the Laferté establishment. So Lady Lyndhurst went her way, and, meeting the fruit of Londonderry’s loins, she said, “Come, Castlereagh, tell me what’s the truth of this horrid story. Talleyrand has just told me that a Bishop was shot last night by several persons unknown. Which of the Bishops was it?” Castlereagh, with that air of careless coxcombry which becomes him so well when speaking to the second sex, answered,” The story is quite true—but, as to your Ladyship’s question, it cannot be easily answered; for the poor Bishop was shot into so many particles, that God alone can tell who or what manner of thing he was.”—“Are any of the shooters apprehended?” said her Ladyship earnestly. “Yes,” said Castlereagh, “and they’ve all been handcuffed—and, to tell you the truth, they look terribly crest-fallen. Indeed, such mere villains are they, that I pulled one of them by the nose myself this morning!”—“A nasty fellow!” cried her Ladyship, “I wish I had hold of him!”—“I wish to God you had, my Lady!” said Castlereagh—and fell speechless on the broad of his back.

3-: Of Sunday 6^th May 1832:

THE SAINT SATIRIZED.

This is a satirical poem, and here’s what we have to say of it. […]
[…]
[…] We shall quote a passage, premising that the poem is a satirical quiz on an amour between a Bishop of London (whether the present or not we can’t nor shan’t say) and a person of the second sex.

4-: Of Sunday 13^th May 1832:

THE THEATRES.

We last week intimated an intention of saying a word on the present state and prospects of theatrical property. We shall do so.
[…]
That fashionable people, who dine at seven or so, and the successive de-gradations of asses who feed at that hour simply because the fashionables do so, should alter the whole of their domestic arrangements, by dining two hours earlier, or disturb their digestive process by devouring a dinner and hurrying to the play, is an idea too ridiculous for any head, save and except one of the Ellenborough “order.” The thing is out of the question. Now and then, when any play becomes the rage, such people will put themselves out of the way: but these exceptions only prove the rule, and do very little for the theatre during a season. And the most interesting part of the performance being generally the first, there is nothing for it but to stow yourself, with a loaded stomach, in a box from seven till half-past ten; when, if you are adorned by any of the second sex appendages, you must probably stop out some afterpiece of bad puns; till, fagged to death, you all return at midnight, mentally revolving the tiresome nature of pleasure.

5-: Of Sunday 10^th June 1832:

THE MAGAZINES.

[…]
LA BELLE ASSEMBLEE.
Edited by la belle Norton, is elegantly got up, and well-suited to the intellects of the second sex.

6-: From The Bell’s New Weekly Messenger (London, England) of Sunday 24^th June 1832:

Proclamation.—Board of Green Cloth.—We order livery slaves to wear only plain clothes. An engraved iron collar round the neck, dog fashion, will answer the good old purpose of shewing to what master man the slave man belongs—We order the second sex to wear a uniform standard bonnet. We of the first sex now are civilized enough to use a nearly uniform head cover. The Quaker helmet will do. Leave gaudy ribbons for children. Savage women love fine ribbous [sic].—We order the Political Unions not to melt, or thaw. The Act of reform is no more a final measure than the act of a wedding is a final measure.—We order the judges to send their mountebank wigs and ermine petticoats to cover the heads and tails of the very respectable monkeys at the zoological gardens.—We order the bishops to wear breeches like men, and not wear aprons like women, and hats like mountebanks.—We order the Times to be consistent for two days. We, lastly, ORDER the self-condemned parliament to go honestly on passing dignity-bills, to show what a venemously [sic] inclined beast the people have compelled to the ‘final measure.’
(Signed) King Halfpenny.