Personality was the combination of characteristics that made a thing an individual. It was related to emotion. The Sixth Doctor once stated that personality changed "probably" due to an imbalance in body chemicals. (TV: The Mark of the Rani)
Robots were not usually given a personality if needed for manual labour or in place of humans (TV: Kerblam! et al.) but some including K9 (TV: The Invasion of Time) and Drathro (TV: The Mysterious Planet) showed some signs of self-awareness and personality. In the case of Robbie, personality was deliberately installed by Carl Readon as an advancement in technology. (COMIC: Doctor Who and the Robot)