Intermediation; acting as an agent or intermediary — the act or business of arranging or mediating transactions, often used in business/distribution contexts.
出版社の取次ぎを通して本が書店に並ぶ。
Books are placed in bookstores through the publisher's distribution/agent (取次ぎ).
その会社は複数のメーカーの取次ぎを行っている。
That company acts as an agent/distributor for several manufacturers.
取次ぎ業者に手数料を支払う必要がある。
You need to pay a fee to the intermediary/distributor.
Answering/receiving on someone else's behalf — e.g., answering the door or phone and ushering a visitor; the act of receiving/connecting someone.
部長は会議中なので、秘書が来客を取り次いだ。
The director was in a meeting, so his secretary received/ushered the visitor.
電話を取り次ぎますので、少々お待ちください。
I'll put you through (answer/transfer the call), so please hold for a moment.
Relaying or passing on a message — conveying information or requests from one person to another.
伝言を取り次ぎます。少々お待ちください。
I'll pass on the message. Please wait a moment.
受付が担当者に用件を取り次いだ。
The reception desk relayed the matter to the person in charge.