The TARDIS (an acronym for Time And Relative Dimension(s) In Space) was a time travelling vessel which had the ability to materialize as a camouflaged object in the timeline it arrived in. The pilot of a TARDIS entered through a set of doors in the camouflaged exterior, to a control and living area which had greatly expanded dimensions compared to the outside.
The Doctor's TARDISEdit
A Type 40 TARDIS was the means of transport for the time-traveler known as the Doctor, and his companions Amy Pond and Rory Williams. It materialized with a loud "vworp vworp" sound and was disguised as a British police public call box. (TNG - Assimilation² comics: "Issue 1", "Issue 2")
It transported them from ancient Egypt to—or so they planned—San Francisco in 1941, but after experiencing dimensional feedback it arrived in a recreation of their intended destination in the holodeck of the USS Enterprise-D in 2368. (TNG - Assimilation² comics: "Issue 1", "Issue 2")
When the Enterprise crossed paths with the Borg-Cyberman Fleet above Delta IV, the Cybermen detected the TARDIS's energy signature aboard the ship. Terrified by the arrival of their foe, the Cybermen accelerated their stratagem and backstabbed the Borg. In response, the Borg proposed an alliance with the Enterprise crew only for Jean-Luc Picard to refuse, only changing his mind when the Doctor took him on a trip in the TARDIS to show him what would happen if the Cybermen assimilated the Borg. (TNG - Assimilation² comics: "Issue 5", "Issue 6")
To restore the Borg, the Doctor used the TARDIS to travel back to the Battle of Wolf 359, downloading a copy of the Borg executive library from Cube 632 before the TARDIS transported a group onto the Cyberman flagship, delaying it long enough for the Enterprise to catch up. (TNG - Assimilation² comics: "Issue 6", "Issue 7")
After the Cybermen had been destroyed and the Borg restored, the Conduit attempted to assimilate the TARDIS only for the ship's consciousness to jump into Data who separated the Borg from the console before Rory and Worf sent him hurtling into the time vortex. After quick goodbyes, the Doctor and his companions used the TARDIS to return to their own reality.(TNG - Assimilation² comic: "Issue 8")
In an alternate reality, two TARDISes were deposited on Earth at some point prior to the 23rd century. In this reality, Emperor Vandar tracked these TARDISes when they arrived in his space-time, captured their occupants, and took the vehicles to his trophy room. One particular TARDIS was also disguised as a police public call box and the other was disguised as an ancient Greek column. Both were present when Vandar entertained Captain James T. Kirk and a landing party, who had been captured along with a number of Legionnaires from yet another reality.
Communications vestibule-disguised time-travel existed in a number of forms. Another time travel device that resembled a telephone booth was part of Vandar's collection. This time machine was in the form of a North American-style telephone booth, from the late 20th century. (TOS - Legion of Super Heroes comic: "Issue 5")
In fiction, a similar machine also resembling the British police box was used by the main character in an old Earth science fiction entertainment series made some time before 2200. It materialized with a loud wheezing, groaning sound. In 2275, Jerry Freeman, Nyota Uhura and Harb Tanzer of the USS Enterprise converted an episode of this series into a three-dimensional hologram in the ship's recreation room. They and James T. Kirk saw the machine materialize and the main character step out and ask if he was in Heathrow. (TOS - Rihannsu novel: My Enemy, My Ally)
In 2369, agent Marion Dulmur of the Federation Department of Temporal Investigations discovered a device that matched the description of this TARDIS in the Eridian Vault, a warehouse of illegal time-travel devices. (DTI novel: Watching the Clock)
A TARDIS is, of course, a reference to the famous time machine of Doctor Who.
The fact that the TARDIS captured by Vandar, or that appearing in the Eridian Vault, was disguised as a police call box suggests that it was the one belonging to the Doctor, as the Doctor's is permanently stuck with that particular disguise. There is the possibility, however, that these are other TARDISes that just happened to take the same disguise (such as The Monk's TARDIS), or that these are from separate alternate universes. The ancient Greek, or "Doric", column disguise, meanwhile, was sometimes adopted by the Doctor's enemy, The Master, for his own TARDIS.
The American telephone booth seen next to the TARDIS appeared to be from Bill & Ted's Excellent Adventure. Bill and Ted's time-travelling phone booth was itself a parody of Doctor Who's TARDIS.