Attribute-based credentials refers to cryptographic systems where someone can produce a proof that they fulfill a certain attribute. Canonical examples are things like an employee ID card, where the ID card can produce a proof that they're an employee, have clearance level X or are part of group Y without the proof containing any information beyond that. Another example would be things like national ID cards, where you could make a check for "is older than 18 years" and the system only receives a cryptographically-verifiable answer to that question, without being able to infer anything else.

Indeed the attribute-based nature of IRMA makes it more general than OpenID Connect. Users can collect all sorts of attributes in their IRMA app, and then selectively disclose any subset of those attributes, as appropriate to the use case. This includes authentication like OpenID Connect (e.g. the user could disclose a username attribute), but also other use cases such as indeed proving that you are older than 18, or anonymously proving membership of a group (using unlinkability, see below), or providing authenticated personal data such as your address or date of birth.

It doesn't serve the exact same intention openID does. Authentication is part of the spec, but its real power lies in the privacy properties IRMA provides.

You can find a better global overview of the protocol and why it was created on this page: https://privacybydesign.foundation/irma-explanation/

In addition to this, a more technical overview of IRMA and its features can be found here: https://irma.app/docs/overview

The privacy properties. With OpenID connect you have traceability - for example if it was used for a vaccine passport, and said passport was required to enter shops, bars, sports venues.. then it would be very easy for the companies implementing the "point of check" devices to track your movements.

With IDE mix that isn't possible.