Having free rein to choose whatever course of action you want.
From the French, meaning 'white (or blank) paper' - the military term for surrender. The term was previously 'charte blanche'.
It is first recorded by Raby in 1707 (reprinted in the Hearne Collection, 1886):
"Who sent Chart Blanch to make a Peace."
Soon after that we have a citation that gives a clearer understanding of the meaning - from Joseph Addison in The Spectator, 1712:
"I threw her a Charte Blanche, as our News Papers call it, desiring her to write upon it her own Terms."
The term carte blanche has also been adopted in the sphere of the Gothic/romantic novel, where it has a specific meaning, that of an offer by a man to a woman to become his mistress. This meaning presumably relies on the notion that the woman would have the option of spending freely at the man's expense.
See also - other French phrases in English.