She's a friend of my wife's.

Literal

She [topic-は] my wife [possessive-の] one-friend is.

一友人 is an unusual, slightly literary construction: 一 ('one') prefixed to 友人 to form 'a friend / one (of her) friends.' It maps to the English indefinite article 'a' more directly than just 友人 alone, which is otherwise number-neutral. This 一+noun pattern survives in formal or written Japanese (一市民 'a [single] citizen,' 一読者 'a reader') but feels markedly bookish today; conversational Japanese would use 妻の友人 or 妻の友達の一人. Choosing 友人 over 友達 also raises the register — 友人 is the more written/formal of the two near-synonyms.