Martha Jones is a character on the television show Doctor Who, during David Tennant's run as The Tenth Doctor. She was the main companion for Series 3, and was a guest star in several episodes of Series 4, as well as the special The End of Time. She was played by Freema Agyeman, who previously had played a minor character in the episode Army of Ghosts. This was explained as that character being Martha Jones' cousin.
Martha Jones, when she is first encountered by the Doctor, in Smith and Jones, is a medical student in a hospital that has been transported to the moon. Despite the insane circumstances, Martha keeps her cool, and impresses the Doctor with her courage, intelligence and compassion. He rewards her with a trip to England in the 1500s, in The Shakespeare Code, and then she becomes a regular companion. Her time as a companion involves fighting Daleks, Weeping Angels, and The Master, giving her a very good track record. She also became, even more than most female companions, romantically infatuated with The Doctor, which is the reason she eventually leaves him. However, after leaving him, she seems to get over her lovesickness, becoming a Medical Doctor specializing in xenobiology, and marrying former companion Mickey Smith.
There has been a lot written on the internet about Martha Jones, with varying degrees of sophistication. Depending on who you ask, Martha is a weakly written, weakly acted character whose only job is to be a stereotypically heartbroken female. Or, she is the strongest, most competent companion of the new series, whose scientific knowledge and fearless attitude make her a match for The Doctor.
To be fair to both Freema Agyeman and Martha Jones, Doctor Who is not always known for the consistency of its writing. Character-defining moments, which involve dialogue and sober reflection, are often sandwiched between scenes where the characters must run from the episode's monster of the week. I often take poor or uneven character development in Doctor Who in stride, knowing it is sometimes unavoidable given the show's format. In other words, I think Martha is a good character, with some good episodes and some good acting, and I don't overanalyze the occasional lapses in writing or acting.