A voice box is a bio-mechanism that allows a Transformer to talk in English. Without the aid of a voice box, a Transformer can only communicate via electronic noises, which can be interpreted by other Transformers, but not generally by humans, unless you are Raf Esquivel. Or Cody Burns.
Ratchet regretted his inability to repair Bumblebee's voice box, and doubted he'd be able to repair Bee's T-cog as well.
While Bumblebee was able to adjust to his limited form of speech, bringing up the topic of his voice box was still a sore subject for him. He was particularly offended by Smokescreen when he said that his substitute voice box was his signature and he shouldn't want to replace it.
Ratchet mentioned Megatron's destruction of Bumblebee's voice box as one of the reasons for refusing to help perfect the Synthetic Energon formula for him.
Upon realizing that Blastwave was unable to speak except through grunting and Cybertronian Sign Language, Bumblebee thought that the bounty hunter's voice box was also damaged like his had originally been.