Before Helena joins the school as a teacher, we learn that she was involved in the death of Jonas' parents. At the beginning of the film, we watch her drive straight toward a couple on the wrong side of the road, causing them to swerve their car into a tree — though we don't know why. Knowing that she was involved in a murder should have prepared us for the future revelation about her identity, but alas, it's such a twist that few probably saw it coming.
At one point in the film, Nina not only infers that Helena had something to do with their teacher's injury, but also she pieces together the mystery of Helena's identity. In an old yearbook, she finds a photo of a teacher named Maria Roth, who looks identical to Helena. However, before Nina could learn more, Helena kills her.
We eventually learn that Helena, was in, fact Maria Roth's daughter by Friedrich, meaning Helena is Jonas' aunt. According to Helena, her mother was deeply in love with Friedrich, who wasn't emotionally invested in their affair. When Friedrich refused to step up after getting Maria pregnant, Maria ended her life, and Helena grew up to seek revenge on Friedrich and everyone he loves — including Jonas.