Marietta's mother is Madam Edgecombe, who helpped Cornelius Fudge and Dolores Umbridge take control of Hogwarts. Madam Edgecombe works in the Floo Network Office, which is part of the Department of Magical Transportation in the Ministry of Magic, and she policed the Hogwarts fires, except for Umbridge's, to make sure that nobody in the school made contact with anyone the Ministry did not want them to have contact with.
As Cho had a romantic intrest in Harry Potter, who was at the center of the Ministry's smear champaign, this left Marietta in a very terrible possition. Marietta joined Dumbledore's Army entirly because of peer pressure. Dumbledore's Army was doing the one thing the Ministry didn't want to happen; training students in combat.
Eventually, Marietta betrayed the D.A. to Umbridge, however, the parchment that all members had signed had been jinxed by Hermione, so she broke out with pimples which spelled the word, "SNEAK." Umbridge took Marietta to testify aganist Harry, but Kingsley Shacklebolt modified her memory, to keep Harry and his friends out of trouble.
This incident caused a rift in Harry and Cho's relationship. Harry blamed Marietta, though not Cho, for the results of her betrayal, but Cho insisted that was it hard for Marietta having a mother in the Ministry and blamed Hermione for jinxing the parchment. It is never explained what happened to Marietta after she betrayed the D.A.