The "Final Experiment" was an experiment conducted by the Cult of Skaro to revive their dying race.
History
Following their defeat at the Battle of Canary Wharf, the Cult of Skaro travelled back to 1930 Manhattan.
Humans with low intelligence became pig slaves used only for manual labour, while humans with superior intelligence became part of the "final experiment". The notion was to create a new Dalek race born from the combination of Human and Dalek DNA, a human-Dalek hybrid.
The Cult succeeded in transforming Dalek Sec into a Human-Dalek hybrid but with unforeseen consequences. Being part human, Sec was able to feel human emotions like sorrow and mercy. Originally Sec had intended to transform every human (with high intelligence) into a hybrid like himself, and for the Earth to become the new Skaro. The hybrids were to be made from humans with above average intelligence who had been captured and had their minds wiped, ready to be programmed with the emotionless Dalek way of thinking. The impact of these new emotions caused Sec to abandon his plan. He appealed to the Doctor for help, asking him to take the Cult of Skaro to a new world. One where they could rebuild their civilisation without the hatred and prejudice of the original Daleks. This plan would have worked by having them become like the new Dalek Sec, and have human emotions but a Dalek brain. Unfortunately, the rest of the Cult no longer saw Sec as being a true Dalek and so betrayed him. The Tenth Doctor considered the failure of the final experiment to be a tragedy. (TV: Evolution of the Daleks)