Why would a client need our CSR file?

I am a beginner to TLS/Ops.

Our operations team have setup a number of virtual hosts with domains we own for hosting endpoints on our Cloud.

We have 3 virtual hosts-

  1. internal – to be used internally for integration purposes with the other departments in our organisation like Siebel CRM…
  2. partner – for organisations with which we do business.
  3. public – as the name suggests

All communication is over TLS.

There is a new partner to whom we(I am a developer) have exposed a new API.

When a developer from their team tries to consume our API with Postman, all he gets is –

Client Certificate is not trusted in this subdomain and/or this endpoint explicitly

Their postman console shows this as seen in the attached image-

enter image description here

In the communication which our OPS team had with the client OPS team, I see that our Ops requested for a CSR file from the client and vice versa.

From the web, I see that a certificate signing request (CSR) is one of the first steps towards getting your own SSL Certificate.

Why would a client need our CSR file and similarly why would our Ops need theirs?