They had an idea that the internet would be based on a system of federated directories, which would be used to find X.400 addresses for people and send them messages on the information superhighway.

This never happened, but parts of X.500 are everywhere. X.509 was one of the requirements for secure access to the directory which was recycled into certificates for the web by Netscape. LDAP is another offshoot, designed for organizations to have their own internal directory internally without needing all the other parts of X.500, and it shares some aspects of the data model with X.500 and so certificates. Active Directory builds on LDAP.

Fun fact: Microsoft Exchange Server had X.400 messaging support up to I think 2016 edition and I have sent an X.400 message even. However the format is pretty cumbersome: C=CH;L=Zürich;O=Zahllos;OU=Zahllos Internet Commentary Division;G=Zahllos is not a nice way to present a contact address. If the C=CH,L=Zürich look a lot like LDAP attributes and/or fields in a certificate, they are.

The ITU do many other things around telephony and communication, and the most obvious one is looking after country codes for phone numbers. If you decided to make a country tomorrow, the ITU would be where you'd go to get your country code delegation. E.164 is their standard for international numbers beginning with a +.