Local citations are mentions of your business name, address and phone number on other websites, such as maps apps, directories, the chamber of commerce and local news. Search engines compare them to confirm that your business is real and is where it says it is. The details should match everywhere, which is what people mean by NAP consistency.
A citation does not need a link to count. What matters is that every copy agrees. An old phone number on three directories and two spellings of your street name make Google less sure which business is which, and less willing to show you.
NAP is name, address, phone. Keep one canonical string for each and use it verbatim on the site, in structured data and in every listing. Mark the contact details on the site with LocalBusiness JSON-LD, or a subtype such as Dentist or RealEstateAgent, carrying name, address as a PostalAddress, telephone in international format and sameAs links to the major profiles.
Aggregators feed many directories, so fix the source before the copies. Audit by searching the phone number in quotes, then old numbers and old addresses. Claim or correct every result. Avoid call-tracking numbers in listings, since a different number per directory is exactly the inconsistency Google is trying to resolve.
{"@type":"Dentist","name":"Riverside Dental","telephone":"+44 20 7946 0123","address":{"@type":"PostalAddress","streetAddress":"12 Market Square","addressLocality":"Richmond","postalCode":"TW9 1AA"}}