If there is a specific person in your firm who looks after a client, you can mark them as the client manager.

From the details tab of the contact's profile, you will see a section for the client team.
Clicking edit will allow you to choose a new client manager, or an existing one.

The client manager is separate to the client owner. Both fields can be left blank if they are not relevant to your team.

This field is most useful if you want to filter work items on your Kanban board by client manager. This will then show all work items for clients that are managed by the staff member/s you identify.

Further reading:
Adding a client owner