The firm pool holds clients your firm has but nobody has been allocated yet. Two things put a client there: an import where you chose Leave in the firm pool, and a departure where a file stayed with the firm without being handed to anyone.
Finding the pool
When the pool has anything in it, a “N in the firm pool” button appears above your client list. Click it to open the pool. Every member of the firm sees it, not just admins. When the pool is empty the button isn't there at all.
Firm owners, co-owners and admins can also reach it from Firm pool in the firm console panel.
Claiming a file
Click Claim on any row. The file becomes yours: it joins your client list, its court dates sync to your calendar, and its match alerts start coming to you. You don't need an admin to do this: nobody was holding the file, so nobody loses it.
If two of you click Claim on the same file at the same moment, the first click wins and the second is told the file has already been taken.
Allocating a file to someone else
Owners, co-owners and admins see a member dropdown instead of a Claim button, so they can put a pool file on whoever is actually acting. That stays admin-only on purpose: it changes whose alerts fire, and the person it lands on didn't ask for it. (They are notified.)
While a file sits in the pool
It is still watched. Court-list matches for a pool client go to whoever your firm nominated under Unassigned Client Notifications in firm settings, so nothing goes unnoticed while the file waits for someone to pick it up.
The Firm view: another door to the pool
You can also claim or assign pool files without leaving the Clients page: switch it to Firm, choose Unassigned in the Filter dropdown, tick the files and click Assign to me or Assign….
Any member can assign from there, including to a colleague. Same files, same result; use whichever page is closer to hand.