She likes the way she looks.

Literal

She [topic-は] her own figure [object-を] is-pleased-with.

気に入る (literally 'enter one's 気 / mind') is the standard idiomatic verb for 'to take a liking to, to be pleased with.' Despite using を on the object, 気に入る is grammatically intransitive in form — を marks what one comes to like, not what one acts on. With ~ている, 気に入っている describes the resultative state of having taken a liking — 'is pleased with, likes.' 姿 ('figure, appearance, form') refers to one's overall visible self.