A certification authority is a trusted third party who confirms the identity of an organization. The CA will first satisfy itself that an organization is exactly who or what it claims to be, and will then issue that organization with a 'certificate'. The certificate is likely to be in the form of an electronic key or value. It can be presented electronically to the CA for verification and confirmation at any time by a trading partner. In some ways the certificate is analogous with a credit card. Both the certificate and the credit card allow two parties to trade with some degree of security without any further proof of identity.
An example of a free software Certification Authority written in Python is pyca.