A servant was a paid staff member. There were various different roles servants were set to perform.
Many servants were loyal to their masters. For example, Chip was loyal to the point of death (TV: New Earth) and Nimrod served throughout many ages. (TV: Ghost Light) Lady Me's servant Clayton came immediately whenever he was called. (TV: The Woman Who Lived)
Other servants continued their role, hoping for an ultimate goal. For example Condo continued his servant-ship to Solon, in hope for the return of his arm. (TV: The Brain of Morbius) Cuthbert Simpson held his role as he awaited the arrival of the Eighth Doctor. (PROSE: The Banquo Legacy) Matilda, a servant of Lady Jane Grey, saw fit to murder her queen for a "greater good". (TV: Lost in Time)