"Colourist" is a title which refers to two distinct positions — one for television work and one for comic strips.
Further information about colourists' work Series 5 onwards
As regards televised work, a colourist (more often called a colour grader or grader in the United States) is a post-production artist who provides one of the final steps in completing an episode of Doctor Who. Because principal photography occurs in a variety of lighting circumstances, individual scenes can have obviously different tonalities. It's the job of the colourist to achieve a colour balance, or "match", across all the scenes. The colourist will usually work closely with the director to achieve a particular colour "pallette" for an episode. Some episodes will tend to hue towards warm reds and yellows, while others will require a darker blue or green palate. The choice of pallette greatly affects the overall mood of the story.
It is well documented in Doctor Who Confidential and various episodic commentaries that producer Phil Collinson asked his grader to generally push up the reds and yellows so that Doctor Who would appear bright and inviting to a viewer flipping through channels on the television set. Nevertheless, certain episodes produced by Collinson, notably Tooth and Claw have an obviously darker tonality.
Colourists were not commonplace or credited on the 1963 version of Doctor Who. In fact, the practice of recording on film whilst on location, and video whilst in studio made full colour grading impossible. However, each episode of the BBC Wales version makes extensive use of colour grading and an artist has been credited for every episode since Rose.
With comic strips
When discussing comic strips, a colourist (more often colorist, due to the predominance of Americans in the industry) is the person who adds colour to images that have been pencilled and inked, usually by other artists. Though traditionally done with physical media, colouring is now mostly done digitally. Modern approaches narrow the gap between what a film colourist and a comic colourist do. Additionally, modern tools give the comic colourist a power with lighting panels that is not unlike that of a cinematographer. If the penciller and inker are mostly in charge of depicting what happens in each panel, the modern colourist creates the mood, not by simply adding colour, but also by adding textures, layers and lighting effects.