in a subdued voice; lowering one's voice
Describes speaking quietly, often to avoid being overheard or to show discretion. The phrase is a set expression using the verb 忍ばせる (to conceal, to keep hidden) in the te-form.
He told me the secret in a subdued voice.
Please speak in a low voice in the library.
The expression combines 声 (voice) with the te-form of 忍ばせる, the causative form of 忍ぶ (to conceal oneself, to hide). The literal meaning is 'making one's voice hidden,' which naturally extends to speaking in a subdued or lowered voice.