Certificate means the electronic evidence that ties a person (e.g. with their ID-card, mobile-ID, digi-ID) to the right to perform legally binding acts (making bank transfers, signing contracts, etc.). In other words, the certificates are necessary to give us the reassurance that an activity or transaction was performed or a signature was given, etc. by the right person.
The person whose ID-card is in the reader is identified immediately when you try to initiate an activity requiring identification. For example, you log in to your bank account or launch the ID-software on your computer. However, having an ID-card is not enough to gain access: every activity that may have legal consequences for you is tied to certificates for security purposes.