。
She's a complete stranger to me.
Literal
She [topic-は] completely I [possessive-の] not-knowing person is.
私の知らない人 is a relative clause modifying 人 — 'a person I don't know.' Note the の where が would normally go: 私が知らない人 and 私の知らない人 are interchangeable here, but の is common in shorter relative clauses and gives a slightly softer feel. 全く intensifies the statement — not just someone unfamiliar, but a complete stranger.