Of American-English origin, the phrase the sky is the limit means there is nothing to prevent someone or something from being successful.
I have discovered that it originated in a metaphor specifically used in the late 19th century of poker games with ‘a sky-high limit’ on stakes.
The earliest instance of this metaphor that I have found is from The Illustrated Buffalo Express (Buffalo, New York) of Sunday 11th September 1898, which published Horace Greeley’s Friend, The Fly Maker, about Prof. A. T. Parker, “the Nestor of trout fishing and the maker of the finest trout and bass flies in this country”:
The image also appeared in Thief Caught in Poker Trap, published in The Times (Philadelphia, Pennsylvania) of Sunday 5th March 1899; “a secret service man” tells of a poker game he played with a big cattle dealer from Texas:
“The cattleman said he would play me a stiff game like they had in Texas. [..] I counted my money and found that I had an even $3,600, not counting the cash in my purse, which had not figured in the playing. I saw that I could make it $10,000 or nothing, for the cattleman was determined to show what he would do. […]
“‘Make the sky the limit,’ said the cattleman; ‘this is going to be quick action for your money, and the money will all be mine in a minnit. Deal the cards.’”
The metaphor appeared in a different form in Steel Magnate on Year’s Prosperity, about “John W. Gates, a multimillionaire of Chicago and president of the American Steel and Wire Company”, published in the San Francisco Chronicle (San Francisco, California) of Thursday 22nd March 1900:
J. W. Gates, according to press dispatches from New York published last Sunday, was a participant in the recent $1,000,000 poker game in a New York hotel that provoked the comment of the whole country. Isaac Ellwood, who is traveling with him, is also credited with having sat at the table and tried for a few of the $30,000 and $40,000 jack pots. According to the published accounts, there was almost a week of uninterrupted play, with the pretty blue sky as a limit.
The earliest instance of the phrase that I have found is from the title of an article published in The Philadelphia Inquirer (Philadelphia, Pennsylvania) of Sunday 18th March 1900:
MILLIONS CHANGE IN POKER GAME
Chicago Men Flay for Enormous Stakes in New York
JACK-POT WORTH $80,000
Wheat Speculator Wins It With Display of Nerve and Two Sevens
A BLUFF THAT WORKED
The Sky the Limit in His Fierce Struggle With the Cards