Usually introduced by the definite article the, the phrase witching hour denotes midnight, with reference to the belief that witches are active, and supernatural occurrences take place, at that time.

More generally, the phrase witching hour denotes the time, especially the dead of night, when bad or sinister things are believed to be most likely to happen.

This phrase alludes to the very witching time of night in the following from The Tragicall Historie of Hamlet, Prince of Denmarke (London: Printed by James Roberts for Nicholas Ling, 1605), by the English poet and playwright William Shakespeare (1564-1616)—it was in this monologue that the adjective witching was first used to designate a time during which it is said that witches are active and supernatural occurrences take place:

Hamlet.
’Tis now the very witching time of night,
When churchyards yawn, and hell itself breaks out
Contagion to this world. Now could I drink hot blood,
And do such business as the bitter day
Would quake to look on.

The earliest occurrences of the phrase witching hour that I have found are as follows, in chronological order:

1-: From Miscellaneous Poems (London: Printed for the author, and sold by S. Hooper, 1762), by Elizabeth Carolina Keene (1743-1778)—as reprinted in Lapham’s Quarterly:

’Tis the baleful witching hour,
Lo! the moon withdraws her light;
Hark! from yonder mould’ring tow’r
Screams th’ ill-boding bird of night:
Now doth murders dagger gleam,
Murder by the Furies led;
Now to haunt the villain’s dream,
Yawning graves give up their dead.

2-: From Cymon. A Dramatic Romance. As it is performed at the Theatre-Royal, in Drury-Lane (London: Printed for the Proprietor, 1766), by the English actor, playwright and theatre manager David Garrick (1717-1779):

ACT IV.
SCENE, an old Castle.

Enter Urganda greatly agitated.
Urg. Lost, lost Urganda!—Nothing can controul
The beating tempest of my restless soul!
While I prepare, in this dark witching hour,
My potent spells, and call forth all my power—
Arise ye demons of revenge arise!
Begin your rites—unseen by mortal eyes!
Hurl plagues, and mischiefs thro’ the poison’d air,
And give me vengeance to appease despair!
Chorus—(underground) We come, we come, we come!

3-: From Ode to the Sun, by Mr. Cumberland, published in 1776—as reprinted in A Guide to the Lakes, in Cumberland, Westmorland, and Lancashire (London: Printed for B. Law, Richardson and Urquhart, J. Robson, and W. Pennington, 1784):

In the witching hour of night,
Whilst thy pale sister lends her shadowy light,
Summon the naked wood nymphs to my sight.

4-: From Seventeen Hundred and Seventy-Seven: Or, A Picture of the Manners and Character of the Age. In a Poetical Epistle from a Lady of Quality in England, to Omiah, at Otaheite (Dublin: Printed for W. Wilson, 1777), by the Irish poet, playwright and essayist William Preston (1753-1807):

Here Circe’s train, and routs of Comus dwell,
And tipsey revel hears the midnight bell,
In secret orgies of the witching hour,
When zealous cot’ries deep libations pour;
But lest intrusion should the rights profane,
A licens’d Clodius joins the pious train.

The phrase witching hour has come to denote the last hour of trading each month when exchange-traded stock options expire, causing increased trading activity and volatility in the market. This is first recorded in Witching Hour For Investors, by H. J. Maidenberg, published in The New York Times (New York City, New York, USA) of Monday 15^th April 1985:

SUPERSTITIOUS or not, many stock investors have come to regard the last hour of trading on the third Friday of each month as the “witching hour,” a time when the market seems to plunge for no apparent reason. It is also a time when the current month’s Major Market Index options expire.
On March 15, for example, when that month’s M.M.I. options died, the Dow Jones industrial average dropped more than 14 points even though there was no significant market news. Previous expiration dates of the options have witnessed similar downward price “spikes.”