。
She left the baby crying.
Literal
She [topic-は] baby [object-を] made-cry [as is-たまま] [leaving-にしておいた].
泣かせた is the causative past of 泣く (to cry): 'made cry.' まま means 'as is' — the baby was left in the state of crying. ~にしておく combines に (into that state) + する (make) + ておく (leave as a deliberate choice), meaning 'to leave things that way on purpose.' The whole phrase conveys a conscious decision not to intervene: she let the baby keep crying.