The problem it solves
When a landlord is an additional insured on a tenant's policy and the landlord also has its own liability policy, both policies may respond to a claim arising from the tenant's operations. Without clear wording, the two insurers can argue about shares, and the landlord's own policy and its loss history can be touched by a claim that was the tenant's. Primary and non-contributory wording settles the order in advance.
What the words mean
Primary means your policy responds first, up to its limits, before the additional insured's policy is called on. Non-contributory means your insurer will not seek contribution from the additional insured's insurer for the share it would otherwise owe. Together they place the loss, up to your limits, on the policy of the party whose work caused it.
Where it appears
In leases, subcontracts, vendor agreements and franchise schedules, usually in the same sentence that requires additional insured status, and often with a waiver of subrogation. The three travel together because they address the same question from different angles: who is covered, who pays first, and who may recover from whom.
How carriers provide it
Either as a standalone endorsement or as language within a blanket additional insured endorsement. The forms list on your declarations page shows which. If neither is present, a contract requiring it is not satisfied, whatever the certificate says, and the fix is an endorsement request to the carrier.
Umbrella policies
Contracts often require the umbrella to follow the primary policy's additional insured and primary and non-contributory provisions. A follow-form umbrella does this automatically; some umbrellas need their own endorsement. Check the umbrella's forms when a contract names it.
The practical check
Hold the contract's insurance exhibit next to the forms list on your general liability dec page. Additional insured, primary and non-contributory, and waiver of subrogation should each map to a form. Where they do, the certificate can reference the forms and the compliance review passes; where they do not, no wording on the certificate will substitute.