To intervene in a dispute, or in a conversation.
To interrupt a conversation by introducing a different subject or making a comment.
To insert something (or oneself) between other things.
To be inserted between parts or things; to come between.
To offer (one's help or services).
To make a remark or provide information when it is inappropriate or indiscreet to do so, or when one does not have permission or the authority to do so.