[trisham]

Conceptual origins[edit]
Inspired in part by the 1958 film Run Silent, Run Deep, Star Trek screenwriter Paul Schneider imagined cloaking as a space-travel analog of a submarine submerging, and employed it in the 1966 Star Trek episode “Balance of Terror”. Another Star Trek screenwriter, D.C. Fontana, coined the term cloaking device for the 1968 episode “The Enterprise Incident”.

Writers and game designers have since incorporated cloaking devices into many other science-fiction narratives, including Doctor Who, Star Wars, and Stargate.

Source: Wikipedia

Storyline Star Trek episode “Balance of Terror”
The Enterprise answers a distress call from Federation Outpost #4, a monitoring station on the Federation side of the neutral zone with the Romulan Empire. The outposts were established over a century ago and no one has actually seen a Romulan. The Romulan vessel seems to have some type of high energy explosive device as well as a cloaking device to make the ship invisible. When it appears that Romulans bear a strong resemblance to Vulcans, Kirk must deal with a rebellious crew member. He must also engage in a dangerous cat and mouse game with a very intelligent Romulan commander. Written by garykmcd

Source: IMDB

[Bratch]

"Balance of Terror" was also inspired by a Robert Mitchum movie called "The Enemy Below".

Memory Alpha

[Charles Martel]

I think it's correct that the term "cloaking device" was not used in Balance of Terror, with phrases such as "invisibility screen" used instead. Aboard the Romulan ship, it was referred to as a "cloak".

One of the series' best episodes. The later Enterprise Incident is also among the fan favorites.