Full definition
ISO 27001 is defined as: ISO 27001 is the international standard for information security management systems, and its certificate is the most commonly accepted proof that a supplier has independently audited security controls.
ISO 27001 certification means a UKAS-accredited body has audited the supplier's controls against the standard's Annex A and confirmed they operate as documented. It is not a one-off exam - it requires surveillance audits and a full recertification every three years.
The certificate carries a scope statement. Check that the scope covers the actual service you are buying - a certificate that only covers head-office IT does not automatically apply to the supplier's SaaS product.