This word for an interstellar instantaneous communications device hasn’t broken out of the specialist science-fiction linguistic area in which it was created, though in that field it’s one of the better-known terms. It was invented by Ursula K Le Guin:
You remember the ansible, the machine I showed you in the ship, which can speak instantly to other worlds, with no loss of years — it was that that they were after, I expect.
Rocannon’s World, by Ursula K Le Guin, 1966.
She tells the story of its invention in The Dispossessed, published in 1974. The same name and concept turns up in several of her books, for example in this one:
He said in his shrill harsh voice, “What’s that?” — pointing to the ansible. “The ansible communicator, sir.” “A radio?” “It doesn’t involve radio waves, or any form of energy ... What it does, sir, is produce a message at any two points simultaneously. Anywhere.”
The Left Hand of Darkness, Ursula K Le Guin, 1969.
A method of communication across galactic distances that circumvents Einstein’s theory of relativity is a useful plot device, avoiding part of the suspension of disbelief that is required with the faster-than-light transport of physical objects. The idea has been used by other SF writers, notably James Blish with his Dirac communicator; Orson Scott Card, Elizabeth Moon, Vernor Vinge and other writers have borrowed the word itself.
It’s not clear where Le Guin got the name from: some people have read a message into its being an anagram of lesbian; that would be relevant to The Left Hand of Darkness, which deals with androgyny and issues of sexuality, but it doesn’t fit Rocannon’s World and it hasn’t been confirmed as her inspiration. A Usenet message posted by Dave Goldman in 2001 said that he asked her about her inspiration and reports that she told him that she got it from answerable.