When you create a responsibility, you assign a profile option called MO:Operating Unit to the responsibility. This operating unit is the organization that you will be working in. When any user logged into this responsibility that user will be working only within this organization. Anything that is run concurrently, only looks at that organization.
To assign an org_id to a responsibility, log into System administrator or Application Developer responsibility, goto profile option & search by that responsibility name. Look for profile option MO: Operating Unit and assign desired organization to this profile.
Org_id in Apps Tables
All tables that end with _ALL have an org_id column. This denotes what org_id that data is related to. If the table does not have an org_id column then the data is available in all organizations.