To interrupt someone while they are speaking by interjecting a remark or opinion.
会議中に人の話に言葉を挟むのはマナー違反だ。
Cutting someone off during a meeting is bad manners.
彼女はいつも他人の話に言葉を挟むので、話がまとまらない。
She always butts into other people's conversations, so discussions never come together.
少し言葉を挟んでもいいですか。補足すると、この方法はコストがかかります。
May I interject briefly? To add, this method is costly.