Role/Approval Process Connection - Security quesiton

What's the connection between a role and an approval process showing up on the EC > Approvals > Approvals > Monitor Approvals search criteria? I'm sure this is a configuration setup between Approval Process to role, but don't know where this is setup at.

I have researched how our Purchasing Dept is able to view monitor approvals for PurchaseOrders through a certain role.  Our Auditing Dept has requested access to view Monitor Approvals for PurchaseOrders, so I attached the only permission list attached to the role to the auditng department role and that didn't give them access.  I then attached the specific role that gives the access and they were able to view it.