An act of treachery, perpetrated on a previous partner in a deceit.
The term 'double-cross' has been used in various contexts for many centuries, usually as a straightforward reference to the shape of two crosses, as in the architectural design of cathedrals for example. That meaning is unrelated to the current figurative 'cheating' usage of 'double cross', which dates only from the late 18th century.
To find the origin of the expression 'double cross' as it is now used, we need to look first at one of the many meanings of the noun 'cross'. From the mid 1700s, a 'cross' was a transaction that wasn't 'square', i.e. not honest and fair. The term was most often used in a sporting context, where a cross was a match that was lost as a result of a corrupt collusory arrangement between the principals involved. You might expect that a 'double cross' was a deceit in which two parties collude in a swindle and one of them later goes back on the arrangement, crossing both the original punters and his erstwhile partner in crime. Although that is the case, the term 'double' doesn't here mean simply 'two times'. 'To double' had long been used to mean 'to make evasive turns or shifts; to act deceitfully'. This derives from the imagery of someone doubling back over a previous route. This 'doubling' gave rise to the term 'double dealing', which has been used since the early 1500s to refer to someone duplicitously saying one thing and doing another, for example, a 'double agent'.
Given that, by the mid 1700s, the language included both 'cross' and 'double', it wasn't a great leap to introduce the term 'double cross' to refer to aggravated duplicity. Double crossing dealings are the precise opposite of those that are 'fair and square', but the two expressions do have one thing in common - they are both tautological. 'Fair' and 'square' both mean honest and 'double' and 'cross' both mean dishonest.
The earliest reference that I have found to 'double cross' in print is in David Garrick's 1768 farce The Irish Widow. The play centres on various practical jokes, and the phrase occurs as a play on words between two of the meanings of cross - 'marriage' and 'swindle':
Sir Patrick O'Neale: I wish you had a dare swate crater [dear sweet creature] of a daughter like mine, that we might make a double cross of it.
Mr. Whittle: (aside) That would be a double cross, indeed!
The sporting usage was defined a few years later, in an early self-help tome, written by 'Two Citizens of the World' and 'Containing Hints to the Unwary to Avoid the Stratagems of Swindlers, Cyprians and Lawyers', i.e. How To Live In London, 1828:
"A double cross, is where a boxer receives money to lose, and afterwards goes in and beats his man."
A systematic policy of double crossing was given the UK government's official, if covert, sanction during the WWII. In 1941, MI5 set up a military counter espionage unit called The Twenty Committee, chaired by John Masterman. The naming of this unit clearly linked the double crosses of the Roman numerals for twenty (XX) with one of the unit's aims, which was to 'double cross' Germany by coercing German spies to become English double agents. The coercion was less than subtle; captured German agents were given an offer they couldn't refuse, i.e. feed false information back to Germany or be shot.
During the Cold War, following the publishing of Masterman's The Double-Cross System in the War of 1939-1945, in 1972, the terms 'double cross' and 'double agent' became much more commonplace.