The .ie top level domain is normally used to register domains for Companies, Organizations or Individuals who are based in or have a substantial connection to Ireland.
Depending on the applicant’s legal status, ie company, club, individual etc. there are various categories under which the applicant may register the domain name. For example, a Company may register its own name as a domain, it could register a business name if it has a different registered business name, a trademark it owns or even the name of a product or service it supplies. Whatever the category the applicant is registering under, they must be able to support the application by providing some information or proof of their claim.
This is usually very straightforward, for example a Company registering its Company name would just need to provide their Registered Company Number.