The time stream was the pathway for the movement of time, usually in relation to individual peoples or planets.
The inhabitants of an unnamed planet were in a different time stream from the rest of the universe. When the First Doctor and Ian Chesterton visited the planet, a few minutes passed for them, but the inhabitants lived through their entire civilisation from their rise and fall. (AUDIO: Rise and Fall)
The Graxnix were removed from the time stream by the Tenth Doctor, trapping them between seconds. (COMIC: Hotel Historia)
The Two Streams Facility of Apalapucia used time streams (which was the source of the name). Apalapucians with the Chen-7 plague were kept in the facility in different time streams, allowing them to live out their whole lives in 1 day. This also meant that each patient was kept isolated in a different time stream, but in the same place. (TV: The Girl Who Waited)
Professor Chronotis' TARDIS could interfere with an individual's time stream. (HOMEVID: Shada, WC: Shada, AUDIO: Shada)
While awaiting his death at Lake Silencio, the Eleventh Doctor had the Teselecta send letters to Amy Pond and Rory Williams, River Song, Canton Everett Delaware III, and a younger version of himself. He explained that to deliver the messages himself, it would involve crossing his own time stream, "best not", he remarked. (TV: The Wedding of River Song)
The Doctor's time stream appeared as an open wound in the fabric of reality inside the ruins of the Doctor's TARDIS in the future on Trenzalore, where the Doctor was buried. The Great Intelligence, in the form of Walter Simeon, arrived on Trenzalore, accompanied by faceless humanoids called the Whisper Men, whom he used to bring several of the Eleventh Doctor's friends there to draw him out so he could invade his time stream, turning all of his victories into defeats and having his ultimate revenge. He did so by directly entering his time stream inside the ruined future TARDIS. However, this plan was foiled by Clara Oswald, who followed the Great Intelligence through the wound. Just as he was, she was ripped into countless versions of herself throughout history and saved various incarnations of the Doctor countless times. The original Clara then found herself in a wasteland inhabited by the various Doctors. However the Eleventh Doctor entered the time stream and was able to extract her, though she saw an unknown incarnation. (TV: The Name of the Doctor)
The Grey Man plucked the Doctor's TARDIS from the time streams, possibly meaning that the Time Vortex was composed of time streams in addition to time winds. (PROSE: Falls the Shadow)
The Third Doctor's encounter with the Silurians was a crucial nexus point in Earth's time stream. (COMIC: Final Genesis)
Time streams may have allowed for possible futures or alternate timelines, as the sigil ring allowed Ruath to change time streams and visit the future Earth ruled by Haemovores. (PROSE: Goth Opera)