(covers information from several alternate timelines)
An aircraft carrier was a type of naval warship in Earth's 20th and 21st century. Its design and size allowed for aircraft, including fighters, bombers, and helicopters, to be launched and retrieved at sea. It was characterized by a long, flat "flight deck" which served as a mobile air base, condensing apron, landing strip, and runway into a small space. Many aircraft carriers after World War II were powered by nuclear fission.
In an alternate 1944, during World War II, the San Francisco Bay was home to aircraft carriers of the United States Navy. As Shuttlepod 1 flew into the bay, one aircraft carrier was entering the bay, while the other was anchored near Yerba Buena Island. Later, in New York City, Alicia Travers mistook an uniform patch and a subsequent non-committal statement by Jonathan Archer of Enterprise NX-01, as him having served on USS Enterprise (CV-6), which by that time had been sunk in the Pacific Ocean. (ENT: "Storm Front")
When the crew of the destroyed starship USS Enterprise traveled back in time to the year 1986, they collected nuclear radiation from the reactor of USS Enterprise (CNV-65). This enabled them to recrystallize the dilithium of their captured Klingon Bird-of-Prey. (Star Trek IV: The Voyage Home)
By the 22nd century it had become a tradition in Starfleet that its starships honored their historical namesake aircraft carrier predecessors with representations of them in any of their interiors; Enterprise (CNV-65) was represented as a painting in Captain Archer's ready room aboard Enterprise NX-01, whereas the same vessel was in the 24th century represented as a bas-relief in the observation lounge of USS Enterprise-D. (ENT, TNG) In the 23rd century a representation of Enterprise (CV-6) was displayed in a gallery on the recreation deck of the refit-USS Enterprise (NCC-1701). (Star Trek: The Motion Picture)
The very distinctive profile of the uppermost carrier in the San Fransisco Bay scene in "Storm Front", strongly suggested it was a member of the pre-World War II Yorktown-class to which USS Enterprise (CV-6) had belonged, and after which Gene Roddenberry had named his Star Trek: The Original Series USS Enterprise starship. As she was declared already sunk by Travers, this, historically at least, only left her three class sisters as possible candidates, USS Yorktown (CV-5) – after which Roddenberry had named his starship originally in his 1964 Star Trek is...-pitch – , the scaled down USS Wasp (CV-7) version, or USS Hornet (CV-8, and the penultimate American carrier to be destroyed in the war), all of which by January 1943 in actuality already sunk by the Japanese Navy, while Enterprise (having participated in all Pacific campaigns, save for the Battle of the Coral Sea) ironically became the sole class survivor and one of history's most celebrated vessels, much like its fictional starship counterpart.
Incidentally, all Yorktown-class sisters were considered by Original Series Producers D.C. Fontana and Robert Justman as namesakes for starships belonging to, what they at the time still called, the Starship-class, USS Yorktown yet introduced into the franchise at a later time in dialog in the second season Original Series episode "Obsession" (though never firmly established in canon as being Constitution-class). The annotations on their memos, made it very clear that the two Star Trek staffers had indeed very much the WW II carriers, and not any other, previous historical vessels, in mind when making the name suggestions, as was evidenced by the remark Justman made on his memo of 9 August 1967, which read, "I think there would be several other candidates, such as Saratoga and perhaps another English carrier, a French carrier, a Russian carrier and certainly a Japanese carrier [note: Though there had been plenty of historical Japanese aircraft carriers to choose from, the eventually chosen USS Kongo had in actuality been a World War I-II era Japanese battleship, whereas the Russians had up-till that point in time not yet operated a carrier]." (The Making of Star Trek, pp. 164-165) That the minds of the Star Trek producers, those of Roddenberry and Justman in particular, were preoccupied with aircraft carriers should not come as a surprise if one realizes that for their generation of Americans, Yorktown, Enterprise and Hornet were household names (as acknowledged by Alicia Travers' instant recognition of Enterprise in "Storm Front") and veritable instant celebrities for two signature 1942 actions; the April morale-boosting Doolittle Raid (in which Yorktown did not participate) after the devastating Japanese raid on Pearl Harbor (only missed by hours by Enterprise), and the even more signature, fortunes-of-war turning, June Battle of Midway, in which the three sisters attained near-legendary status overnight, even though Yorktown was lost in the battle (Wasp was transferred from the Atlantic to replace her, only to be sunk herself a mere three months later).
Other Constitution-class vessels named after aircraft carriers include,
- USS Lexington – after USS Lexington (CV-2), Lexington-class (class-sister of the by Justman suggested Saratoga) and USS Lexington (CV-16), Essex-class, the latter being renamed from USS Cabot to honor the former when lost in the Coral Sea (as were class-sisters USS Yorktown (CV-10), USS Hornet (CV-12) and USS Wasp (CV-18) in honor of their by then lost Yorktown-class predecessors).
- USS Intrepid – after USS Intrepid (CV-11), Essex-class.
- USS Constellation – after USS Constellation (CV-64), Kitty Hawk-class, and the only post-WW II carrier in the list of name suggestions.
- USS Eagle – after British carrier HMS Eagle, no class.
USS Essex (after USS Essex (CV-9), class vessel) nearly made the cut as it was already featured in the first draft treatment of the script, dated September 30, 1967 for the second season episode "Journey to Babel", which contained a line having Lieutenant Uhura state,
- "Star Fleet Command confirms alien attack on the other starships, Sir. The enemy was defeated. Starships Essex and Eagle suffered heavy damage, but will make base."
The reference though, was dropped from the episode as aired , but USS Eagle, referenced in the "Operation Retrieve" mission charts, resurfaced a quarter of a century later in Star Trek VI: The Undiscovered Country, courtesy Michael Okuda.
In Star Trek IV, the "part" of USS Enterprise (CNV-65) was actually filled by the conventionally-powered USS Ranger (CV-61, Forrestal-class), because Enterprise was on deployment at the time of the movie's filming. (Star Trek Encyclopedia, 1997, p. 137)
The painting of Enterprise (CNV-65) in Archer's ready room was one of a series of four illustrations, depicting the historical lineage of Enterprise, made by Production Illustrator John Eaves, who, due to his own oversight, had only 24 hours to produce the drawings. Actually, Eaves had produced a series of five; however, due to space limitations on the wall, one had to be left out. The one chosen to be left out portrayed Enterprise (CV-6).  Set Decorator James Mees recalled of the ready room, "We were trying to show that [Archer] was someone who had a past, a good past, and who remembered that past; that's what the show is so much about." (Star Trek: The Magazine Volume 3, Issue 3, p. 85)
The shooting script for Star Trek: The Motion Picture described the length of the long range shuttle Surak to USS Enterprise (NCC-1701) as, "about the size of a figher aircraft floating in over the vastness of an aircraft carrier".