Do you remember what she was like?

Literal

She [topic-は] what kind person was [question-か] remember [question-か]?

An embedded wh-question (どんな人だったか) inside a 覚えていますか ('do you remember') frame — a doubled-か structure that's normal in Japanese, since the inner か serves as a noun-phrase particle for the embedded question and the outer か marks the main-clause question. 覚えている ('remember,' literally 'is in the state of having committed to memory') is one of the resulting-state ~ている verbs, where the past act of memorising is felt in the present remembering.