A manual how to split consolidated external identities in Perun used to be here. It contained many warnings advising users not to do it without proper consideration (and preferably, not to do it at all). Users didn't care. So the manual is simple now: kindly contact user support.
A user should ideally have a single identity in the Perun user management system. This Perun identity can be created using an external identity. An external identity is an identity from user's home organisation, LDAP, or other sources. One or more external identities can be connected to a single Perun user. E.g. Perun user A can have external identities from an employer (e.g. CESNET), a university, Google, Facebook and so on.
As we are legally allowed to provide our services to a restricted community (“academic community” is a reasonable approximation), our users have to prove that they belong to the community from time to time. They usually do so logging in using one of the external identities. It is most likely an identity supplied by a university where the user works and/or studies. Other connected identities can be used for logging into services on daily bases.