As the Ninth Doctor once told Rose Tyler, the translation circuit was a "gift of the TARDIS, a telepathic field that gets inside your brain — translates." (TV: The End of the World) The Doctor himself was a part of the circuit, without whom the circuit was broken. When the Tenth Doctor was incapacitated due to post-regenerative crisis, for example, Rose lost access to the circuit, and could no longer understand languages she did not personally know. (TV: The Christmas Invasion) Sometimes, the translational circuits would not work for passengers in different timezones. When Nyssa got trapped in the 1950s while the Fifth Doctor and ship were in the '60s, German signs were not translated for her. (AUDIO: 1963: Fanfare for the Common Men)
Exactly who could take advantage of the circuit, and under what circumstances, was variable, suggesting the Doctor could change its settings in some way. The Fourth Doctor told Sarah Jane in Renaissance Italy that it was a "gift of the Time Lord" that he allowed her to share. (TV: The Masque of Mandragora) During the incident with the Sycorax on Christmas 2006, the translation circuit worked for all humans on the Sycorax ship, even though he was not, at the time, apparently aware of their presence. (TV: The Christmas Invasion) On yet another occasion, the Seventh Doctor told Elizabeth Klein that the telepathic field was limited to a certain radius around the TARDIS. (AUDIO: Survival of the Fittest) The translator continued to work after Rory Williams was transported into the past with the TARDIS. (TV: The Angels Take Manhattan)
The Ninth Doctor once mentioned that the translation systems had a swear filter that prevented the passengers from hearing any swear words; even an angry cavewoman's rants were translated as her saying, "Blinking", rather than a more apt phrase. (PROSE: Only Human)
The translation circuit was apparently capable of translating for creatures without a language. The Eleventh Doctor was able to barely communicate with a Krafayis, which were only of animal-level intelligence. (TV: Vincent and the Doctor)
Multilingual individuals were sometimes capable of identifying what language was being spoken. When the Fourth Doctor spent time conversing with Emmeline Neuberger, a native German speaker who also spoke reasonably good English, he responded to her with equal ease when she spoke to him in English and German without showing any sign that he noticed her change in language, Emmeline noting that she couldn't tell what language he was addressing her in. (PROSE: Wolfsbane) The Doctor tended to have more luck in identification. The Fourth Doctor identified the mercenary trader Garron as originating from Somerset simply by hearing his accent, despite the fact that he was on the planet Ribos at a time before it had become aware of other worlds and hence would have no reason for an Earth native to visit it. (TV: The Ribos Operation) On another occasion, the Tenth Doctor used Madame de Pompadour's particular French accent to identify the century in which she lived, while Mickey simply assumed she was speaking English. (TV: The Girl in the Fireplace)
The TARDIS translations were closer to the original language than other translators, although it would allow 'local' translations to take over if languages were already being translated. Selachian battlesuits had built in translators, giving them a harsh voice. When removed from their armour and in range of the TARDIS, their speech sounded more melodic, closer to the Ockoran's natural song-like language. (PROSE: The Final Sanction) Likewise, the translation circuit did not compensate for the glitch in Sil's translation system that caused his voice to sound so disturbing (TV: Vengeance on Varos).
The TARDIS translator gave some individuals noticeable accents. It made Elizabeth Klein, a German-speaker, perceive the Seventh Doctor as having a "stuffy Prussian accent". (AUDIO: Survival of the Fittest) Vincent van Gogh, a native Dutch speaker, assumed that Amy was from Holland due to her having a similar accent to his own. (TV: Vincent and the Doctor)
It has been suggested on some occasions that the TARDIS translation also slightly modified peoples' minds so that they did not consciously register that they should be unable to understand the languages they were listening to. The Doctor was able to deduce that Sarah had been hypnotised when she directly asked how she was able to understand Italian during a trip to the fifteenth century. (TV: The Masque of Mandragora) On another occasion, when the Brigadier asked how he was able to understand German during a trip to a party thrown by the Nazis in Hitler's honour in 1942, the Sixth Doctor reflected that the champagne the Brigadier had drunk was probably responsible for him asking the question. (PROSE: The Shadow in the Glass) Something similar happened with Donna Noble; she asked the Doctor why signs in "Rome" were in English, wondering if he was trying to make her look stupid by bringing her to Epcot. (TV: The Fires of Pompeii)
Failure to translate
Although the circuit could translate a vast majority of languages that it encountered in the universe, there were some instances where the circuit failed.
In his second incarnation, the circuit failed to translate both German and French while on a planet controlled by the War Lords, while it did translate the War Lords themselves. (TV: The War Games) Whilst visiting Vincent van Gogh, the Doctor's TARDIS was covered in posters which remained in French. (TV: Vincent and the Doctor) Of course, it was established that there was a lag in translation of the written word. (TV: A Good Man Goes to War)
Even some Earth languages did not translate. In the time of the Fifth Doctor, the TARDIS was unable to translate for Kurkutji, who spoke an old Aborigine dialect, although the Doctor's companion Tegan Jovanka was able to speak the language normally through personal knowledge. (TV: Four to Doomsday)
Some languages that were too complex, like the Sittuun language encountered by Amy and the Eleventh Doctor, would not be translated. (PROSE: Night of the Humans) In other instances, if the idea was too complex, translation would be incomplete or faulty, an example being when the Fifth Doctor used the phrase, "We will have been here before", to describe the TARDIS arriving at a crater on the Moon in the early twenty-first century when the TARDIS would visit that location in 1878 in its personal future. (PROSE: Imperial Moon) The Seventh Doctor and Mel encountered Golosian, which was also too complex to be translated. (AUDIO: Bang-Bang-A-Boom!) The Foamasi language also went untranslated. (TV: The Leisure Hive) This was apparently due to the complexity, as the language stimulated the visual cortex of the brain, meaning Foamasi effectively saw their language. (PROSE: Sleepy)
Even later, languages which predated the universe could not be translated. The script written on the planet Krop Tor was not translatable. (TV: The Impossible Planet) A very old minotaur-like species couldn't be translated properly. Its words sounded like roars and grunts to the companions, and the Eleventh Doctor had difficulty understanding several words. (TV: The God Complex)
Translation could be affected by the listener, as when the circuit initially failed to allow Anji Kapoor to understand the language of the intelligent tigers of the planet Hitchemus, although this was revealed to be because Anji couldn't accept that the Tigers were sentient. (PROSE: The Year of Intelligent Tigers)
User interaction with the circuit
When the Tenth Doctor and Donna arrived in Pompeii, Donna wondered what would happen if she spoke Latin to the locals, whose native language was Latin. Instead of hearing Latin, at least one native speaker of Latin believed her to be speaking Celtic. (TV: The Fires of Pompeii)
Most of the Doctor's companions were native speakers of English, and the Doctor himself was a "master of English" — indeed a fan of the language. (AUDIO: ...ish) However, he did occasionally travel with non-English-speakers. Elizabeth Klein, a native German speaker, required the circuit just to communicate with the Doctor. (AUDIO: Survival of the Fittest)
The circuit could apparently be influenced by the passengers who travelled in it. When the Eighth Doctor, Fitz and Anji landed on a world where they encountered the "mooncalfs" - people born with some kind of genetic deformity, regarded as an abomination in this world - Fitz recalled the term from his childhood as referring to someone who was either a bit slow or someone considered a freak, speculating that the TARDIS translator chose a word that he knew to describe them because it was more "tuned in" to his "wavelength" given that he had spent longer travelling with the Doctor than Anji. (PROSE: Vanishing Point)
Anji had a particularly unusual relationship with the translation circuit. When dealing with the sentient tigers of the planet Hitchemus, she was actually able to ignore the circuit's attempts to translate at first because she initially couldn't accept that the tigers were sentient. (PROSE: The Year of Intelligent Tigers) She actually learned a new language whilst travelling with the Doctor. Caught in the midst of the Spanish Civil War, she used her pre-existing fluency in French to quickly assimilate Catalan while she was in Barcelona. (PROSE: History 101) It was unknown how she was able to experience traditional language learning whilst still nominally linked to the TARDIS.
Before travelling with the Eighth Doctor, Mary Shelley had been trying to learn German. When she travelled to Austria with the Doctor, she assumed that she was just picking up German faster when she could easily read the newspaper. (AUDIO: The Silver Turk)
When travelling with Jago and Litefoot, Litefoot immediately noticed that the Venusians were speaking English when they should be speaking an alien language. Jago, on the other hand, thought Venusians would naturally speak English. (AUDIO: Voyage to Venus)
Behind the scenes
The TARDIS crew's ability to understand other languages wasn't explained in any story in any medium until The Masque of Mandragora. Even so, that was the only story in the whole of the 1963 version of Doctor Who to even touch upon the subject of language translation. The issue has had much greater prominence in the BBC Wales programme, which has then had an impact on the Big Finish past Doctor stories.