。
She has a serious illness.
Literal
She [topic-は] serious illness [to-に] has-caught.
病気にかかる (to catch/contract an illness) is a set expression — かかる here means 'to be affected by' rather than its other senses (to take time, to hang). The ~ている marks the resulting state: she caught the illness at some point and is still ill. The contrast with 病気になる (became ill, framed as a one-time change of state) is subtle but real — かかっている focuses on the ongoing afflicted condition, while なった emphasizes the moment of transition into illness.