。
She soothed the baby to sleep.
Literal
She [topic-は] baby [object-を] soothing made-sleep.
あやす means 'to soothe' or 'to comfort' a baby — rocking, patting, singing, or making gentle sounds to calm a fussy child. 眠らせた is the causative of 眠る (to sleep): 'made/helped to sleep.' The te-form あやして connects the two actions as a sequence: first she soothed, then the baby fell asleep. This is a warm, domestic scene with vocabulary specific to infant care.