ISNI and other database identifiers fit under the topic of authority control.
The idea is you have a unique identifier in a database that uniquely identifies that person / idea / thing.
If two people share the same name there can both have an entry in the database and a unique identifier.
ISNI seem to be designed for national libraries where if you publish a book they will give unique identifiers to you as the author and list what you have created.
These databases tend to link to each other so if you know one identifier you can look up the record and find it in another database.
For example Daft Punk have a musicbrainz id, an ISNI, VIAF, wikidata identifiers.
If you look up the ISNI you can find the VIAF and from this you can find wikidata.
From wikidata you can find all the other id’s including musicbrainz.