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Humanised Daleks were, as the name suggests, Daleks implanted with the Human Factor as isolated by the Second Doctor. The Factor caused significant changes in the behaviour of the creatures, which led to a enormously destructive Dalek Civil War which for a time put the future of the species in doubt.
The original humanised Daleks received the Factor from positronic brains constructed by the Doctor. The nature of the relationship between this machine intelligence and the organic brain of the Dalek creature is unclear. Later, mass-implantation of the human Factor was contrived by the Doctor, suggesting it was possible to directly alter the nature of a Dalek without the use of technology such as the brains. (TV: The Evil of the Daleks)
Large numbers of humanised Daleks were seen in their colony on Kyrol, but it is unknown whether the new Daleks spawned in the colony needed implanting with the human Factor, or if humanisation could be an inherited trait. (COMIC: Children of the Revolution)
Humanised Daleks behaved fundamentally differently to the rest of the species: they were non-conformist, sometimes playful, frequently questioned orders, and lacked instinctive obedience to their superiors. Perhaps most unusually, they showed no signs of the intrinsic Dalek desire to destroy all other life-forms, or the self-destructive psychosis which tended to afflict Daleks who acquired physical or behavioural traits from other species. It was suggested that it was this which allowed them to realise their full psychokinetic potential. (TV: The Evil of the Daleks)
Origins and history
The discovery of the Human Factor
As part of a typically devious scheme, the Daleks recruited the Doctor to discover those traits which epitomised the essence of the humans who had so often defeated them. The Doctor was told that the Daleks planned to assimilate this 'Human Factor' into themselves, but in fact the plan was to use it to define the quintessential Dalek Factor and introduce this into the human race instead.
The Doctor successfully determined the nature of the human Factor and implanted it into three test Daleks known as Alpha, Beta, and Omega. These original humanised Daleks were later reintegrated into the population on Skaro. Inevitably, one of them questioned a routine order given by a superior.
The Dalek Emperor realised that independent thought was anathema to Dalek culture and civilisation and that the humanised Daleks were a deadly threat. It ordered that all Daleks be re-implanted with the Dalek Factor - but the conversion system had been sabotaged by the Doctor, and rather than reinforcing the Dalek Factor, many Daleks were exposed to the human Factor instead.
Led by Alpha, Beta, and Omega, the humanised Daleks approached the Emperor, demanding to know the reasons for the orders with which they they were constantly being issued. Fighting broke out between them and non-Humanised Daleks, which rapidly escalated into a full-scale war throughout the Dalek City. Even the Doctor, who was largely responsible for the conflict, believed the fighting would only end with the final destruction of the Dalek race. (TV: The Evil of the Daleks)
Azhra Korr, and the final sacrifice
However, the unmodified Daleks were too numerous and the surviving humanised rebels, led by Alpha, were forced to flee Skaro in a captured saucer. Alpha had a vision of a world where they could live in peace and seclusion, knowing the rest of their species would never stop hunting them. They settled on Kyrol in a subterranean city, Azhra Korr, beneath the sea bed. Here they created their own culture, making art, meditating, and developing the psychic abilities latent in all Daleks.
Many years later a human submarine was disabled by a mysterious electromagnetic pulse and the Daleks intervened to save them. They were delighted to learn the Doctor was also aboard, as they considered him their saviour. However, their need to remain secluded meant that neither the humans or the Doctor could ever leave the city again, and Alpha extracted a promise to this end from the Doctor.
However, the saviour of the Daleks broke his word and attempted to contact the humans on the surface of the planet. At the same time paranoia and distrust was spreading amongst both the humans and the humanised Daleks. The Doctor eventually discovered that the Daleks had been duped by Kata-Phobus, the last native Kyrollian, an immensely powerful psychic creature. Kata-Phobus had sent Alpha the vision of Kyrol, luring the Daleks here so they could prosper and multiply - before harvesting them for their vast reserves of psychokinetic energy and going on to destroy the human colony as well.
Alpha and the other Daleks refused to let themselves be used this way, opting to self-destruct en masse - the interruption in Kata-Phobus' feeding cycle killing the Kyrollian, even though it meant the sacrifice of every known humanised Dalek. (COMIC: Children of the Revolution)
Similar examples after the Time War
Similar phenomena occurred with Daleks after the Last Great Time War, but on account of different circumstances. In one instance, one Dalek drone (nicknamed Metaltron by its captor, Henry van Statten) experienced a flood of human emotions after extracting DNA from Rose Tyler. This drone eventually considered emotions to be unbearable "sickness", and asked for the order to commit suicide. (TV: Dalek) Later, the leader of the Cult of Skaro, Dalek Sec, engulfed the human Mr. Diagoras and underwent a "Final Experiment". He became an entirely new creature, a Human-Dalek, who felt all the emotions of humans. A force of "Dalek-humans" (human shells with Dalek minds but with a bit of Time Lord DNA that gave them free will) was also created. However, Sec and the "Dalek-humans" ended up questioning their species' xenophobia and ruthlessness, and were exterminated by the other pure-Dalek members of the Cult of Skaro. (TV: Evolution of the Daleks)