Whatever you feel towards Martha Jones as a character, love her or loathe her, you can’t ignore the fact that she was a milestone character for Doctor Who, both for the revival series and the series as a whole. She was the first full-time companion of colour, the first female companion of colour and the first revival Companion with siblings - still is, in fact. Her series (series three) also marked the return of the Master, an increased focus on both the Time Lords and the effect the Time War and the destruction of Gallifrey had had on the Doctor.
However, there’s more to it all than that. I posit, that over the course of series three, Martha Jones was deliberately developed as a character to become a human equivalent of the Doctor.
Episode by episode, Martha’s character arc takes her from being a driven medical student and companion to the Doctor, to being off on her own, defeating the Doctor’s
boyfriend arch nemesis - the Master - and becoming the Doctor in her own right. This is done through references, parallels, costuming, and character/story arc development. Though these parallels are far more thought out during series three and have a deliberate beginning, middle and ending, Martha’s reappearances in five episodes of series four (The Sontaran Stratagem/The Poison Sky, The Doctor’s Daughter, The Stolen Earth and Journey’s End) also draw further parallels between her and the Doctor and even foreshadow the events of the series four finale.