The noun blanket is from Old-Northern-French and Anglo-Norman forms such as blankete and blanket, composed of blanc, white, and the diminutive suffix -ette, and meaning white woollen material, blanket cloth, and blanket.

(The Modern-French word for blanket is couverture, meaning literally covering, from the verb couvrir, to cover. The phrase tirer la couverture à soi (literally to draw the blanket to oneself) means to take all the credit, to hog the limelight. In French, blanquette is mainly used to designate a dish consisting of white meat in a white sauce.)

The English noun blanket is first recorded in the sense of a white or undyed woollen material used for clothing; The Life and Martyrdom of Thomas Becket, Archbishop of Canterbury (circa 1300-1325) contains the following verse:

(1845 edition)
Blak was his cope above: his curtel [= kirtle] whit blanket.

The sense covering of a bed is attested in The vision of William concerning Piers the Plowman, a 14^th-century allegorical dream vision attributed to William Langland (circa 1325-circa 1390):

Cam no wyn in hus wombe · þorw þe weke longe,
Noþer blankett in hus bed · ne white bred by-fore hym.
     in contemporary English:
No wine came to his stomach all week long,
Nor any blanket on his bed or white bread before him.

The phrase to toss (someone) in a blanket, meaning to administer a rough irregular mode of punishment to (someone), is first recorded in The Second Part of King Henry the Fourth (around 1599), by the English poet and playwright William Shakespeare (1564-1616); Falstaff has just forced Pistol out of the Boar’s Head Tavern (Doll Tearsheet is a prostitute):

(Folio 1, 1623)
– Falstaff: A rascally Slaue, I will tosse the Rogue in a Blanket.
– Doll Tearsheet: Doe, if thou dar’st for thy heart: if thou doo’st, Ile cauuas thee betweene a paire of Sheetes.

The first known user of born on the wrong side of the blanket, said of an illegitimate child, was the Scottish author Tobias George Smollett (1721-71) in the epistolary novel The Expedition of Humphry Clinker (London, 1771); in a letter to Mary Jones, Winifred Jenkins, the maid of Tabitha Bramble, Matthew Bramble’s sister, explains that she wants to marry Humphry Clinker, who, it has just been discovered, is Matthew Bramble’s illegitimate son:

Why not strike while the iron is hot, and speak to the ’squire without loss of time?—What subjection can the ’squire make to our coming together?—Thof my father wan’t a gentleman, my mother was an honest woman—I did’n’t come on the wrong side of the blanket, girl— My parents were marred according to the rights of holy mother crutch, in the face of men and angles.

The term blanket finish denotes a finish of a race in which the contestants are so close together that they could be covered with a blanket. The image is first recorded in the following from The Sporting Magazine; or, Monthly Calendar of the Transactions of the Turf, the Chase, and every other Diversion Interesting to the Man of Pleasure and Enterprize (London) of April 1793:

Description of the Oatland Stakes run on Ascot Heath

Embellished with an exact Representation of the Great Oatland Stakes run over there on Tuesday the 28^th of June, 1791.
The approaching season induces us to give our readers a description of This Race, (of which the annexed plate is a striking representation) the greatest race ever decided in this kingdom; and upon the event of which, upwards of one hundred thousand pounds was won and lost. The original subscribers were forty-one, of a hundred guineas each, half forfeit; two declaring forfeit in the July preceding, paid only twenty-five guineas each. Nineteen started, and twenty paid half forfeit; the exact stakes, therefore, run for in one heat, (and that decided in seven minutes and thirty-three seconds) was 2950 guineas, which fortunately fell into the hands of his royal highness the Prince of Wales, with the odds of 20 to 1 against him. Of the nineteen that started, the judge could only place the first four, for not only those, but four or five others, might have been nearly covered with a blanket.

The expression wet blanket denotes a person or thing that throws a damper over something, as a wet blanket smothers fire.—Cf. ‘wet blanket’: meanings and origin.

In Dictionary of Americanisms: A glossary of words and phrases usually regarded as peculiar to the United States (2^nd edition – Boston, 1859), John Russell Bartlett (1805-86), American ethnologist and historian, recorded the following:

– Blanket. A term used distinctively for the clothing of an Indian. To say of one’s father or mother that they “wore the blanket,” implies that they were but half civilized Indians. (Western)
– Blanket Indian: A wild Indian, whose principal article of dress is the blanket.

The phrase on the blanket was applied to supporters of the Irish Republican cause held in the Maze prison, near Belfast, and elsewhere, who, from 1976 to 1981, wore blankets instead of prison clothes, as a form of protest against being treated as criminal rather than as political prisoners; this was explained in Provos plan protests, published in The Guardian (London) on 14^th September 1977:

Provisional Sinn Fein protests are planned in Northern Ireland today against the removal of political status from paramilitary prisoners.
[…]
The protests mark the first anniversary of convicted Provisional Kieran Nugent’s refusal to wear prison uniform at The Maize, formerly Long Kesh. Mr Nugent was one of the first paramilitaries convicted after political status was ended for crimes committed after 1975. Unlike previous convicts who live in Provisional or Loyalist compound exactly like prisoners of war he was ordered to wear ordinary uniform and to accept common criminal treatment.
His refusal has meant solitary confinement, wearing only a blanket, ever since, according to the Republican movement. They claim that nearly 200 fellow paramilitary prisoners are now “on the blanket” at the Maize and Armagh women’s prison as well as one Mr Shane O’Docherty in Wormwood Scrubs.