Cults were belief-based organisations.
The Cult of Skaro was a cult formed during the Last Great Time War by a group of Daleks to think in manners outside that of the Dalek race. (TV: Doomsday) The Cult of Shining Darkness was formed with the purpose of destroying all robotkind. (PROSE: Shining Darkness)
Some cults were much like religions, formed for/through the worship of a deity; on Earth most such cults took their name from the deity they worshipped. These included the Cult of Vulcan, (TV: The Fires of Pompeii) the Brotherhood of Demnos (TV: The Masque of Mandragora) and the Hecate Cult. (TV: A Girl's Best Friend) One cult worshipped Bernice Summerfield as a deity from its church on a deserted aircraft carrier at the centre of the Medelein Sea on Phraxa. They instigated a galaxy-wide campaign to bring about her death because she wasn't living up to their image of her. (PROSE: The Dead Men Diaries)
Other cults had specific places within their respective societies. The Sibylline Sisterhood was a highly prestigious cult of soothsayers in Pompeii that cultivated the psychic potential of individuals present in the city. (TV: The Fires of Pompeii) The Tong of the Black Scorpion, who worshipped Weng-Chiang, was described by the Fourth Doctor as one of the most dangerous criminal organisations on Earth. (TV: The Talons of Weng-Chiang)
Other cults such as Faction Paradox revelled in being known as a "cult", as a taboo and as an affront to the Time Lords, whose ideologies and practices they actively sought to mock and intimidate. (PROSE: Alien Bodies, Unnatural History)