To interrupt or interject into someone else's conversation; to butt in while others are speaking.
ちょっとだけ口を挟んでもいいですか。
May I just interject for a moment?
彼はいつも人の話に口を挟むので、周りが困っている。
He always interrupts other people's conversations, so those around him are annoyed.
会議中は発言者の話に口を挟まないでください。
Please do not interrupt the speaker during the meeting.