What is authentication, and what determines how strong an authentication is?

Authentication is the recurring process of verifying that a (partial) identity belongs to the subject presenting it; its strength depends on how firmly the identity is bound to the subject, which comes down to the number and type of authentication means used.

Where registration happens once, authentication happens on every access: it checks the claimed digital identity by verifying that the presented credentials belong, with some level of assurance, to that identity.

Strength is not a property of the password alone but of the binding between identity and subject:

• Number of means: one factor (password) binds weakly; two independent factors bind more strongly, because an attacker must compromise both.
• Type of means: something you know (password), something you have (token, phone, smart card), something you are (biometrics). Types differ in how easily they can be copied, guessed or stolen.

Synonyms in German usage: Authentifikation, Authentisierung, and colloquially "login".

Go deeper:

• NIST SP 800-63B-4 Authentication and Authenticator Management — authenticator types and the three authentication assurance levels that grade binding strength.
• Multi-factor authentication (Wikipedia) — the knowledge, possession and inherence factors and why combining them binds more strongly.