Domain registrant verification is needed for any generic top-level domains (like .com, .net, .org etc.). This is an ICANN-mandated process aimed at ensuring the listed registrant for such domain names is always contactable. A rough rule of thumb is that if the top-level domain is longer than two characters, then it usually needs to be verified. It does not apply to country code domains like .ie or .eu etc. Registrant verification is also required for the new top-level domains like .club, .photography etc.

You can check the current contact email address for your domain via any whois utility, for example http://whois.lookup.ie

When verification is required for your domain, an email message will be sent to the contact email as per the whois. You must click the link in this message in order to complete the verification process.

If you do not verify your domain within 15 days, the domain will become suspended. If this happens, the domain status in whois will show "ClientHold" and your domain name will stop working.

If the contact email address on your domain is incorrect, then you will not be able to receive the verification emails. In this case, you need to update the whois information on your domain with an email address that you can receive on. The article linked below tells you how to update the whois information for your domain:

http://support.irishdomains.com/index.php?/Knowledgebase/Article/View/73/3/how-to-update-whois-information-on-a-domain

Once you update the contact email on your domain, a new verification email will be automatically sent to the new address.

See also the following article for more information:

http://support.irishdomains.com/index.php?/News/NewsItem/View/98/registrant-verification-now-required-for-many-domains