She has three siblings.

Literal

She [target-には] siblings [subject-が] three-people exist.

彼女には is the use of には as a topical-target marker: 'as for her, [it is the case that]...' Combined with the existential いる, the sentence reads 'as for her, three siblings exist' = 'she has three siblings.' Japanese systematically uses the existential いる/ある constructions for what English expresses with 'have' — 友達がいる ('have friends'), お金がある ('have money'). 兄弟 ('siblings') is gender-neutral when used as the broad term for siblings of any gender, though it literally combines 兄 ('older brother') + 弟 ('younger brother').