In the comics, Terra first appeared in "The New Teen Titans" (vol.1) #26 and 28. Much like this animated version, she's a troubled and confused girl. She appears to be forced to be working for terrorists until the Titans take her in. Beast Boy specifically reached out to Terra. Terra also had problems controlling her powers, particularly when enraged.
As the Titans go to the Tower after meeting Terra at the rocky canyon, the section where they once stood crumbles apart, as a subtle indication of what Terra will do to them in the climax.
In the comics, Deathstroke [Slade] takes a particular interest in Terra. However, in this series Slade's interest in Terra as his apprentice mirrors his interest in Robin from Season 1.