Put simply, NAP is a shortcut for Name, Address, Phone Number. A variation on the NAP is NAPW or NAP+W, where the W stands for website.
That little cluster of information is a key data point for search engines to understand unique entities. This allows businesses to have many separate locations, and still be part of the group of businesses. It also allows single location businesses to share premises with other businesses and not get confused.
Imagine going to a networking event, and being introduced to someone. They’re introduced as being the owner of a particular business. When they give you their business card you notice a different business name and their business address. As you leave, you pick up their brochure from the members table and notice the address and website is different from the card. Later you look them up on the web only to discover a completely different street address! Wouldn’t it make you wonder?
The same goes for search engines.
If you wish to appear in local search results, one of the first things to check is your NAP is up-to-date and consistent. Start on your website and then look at other places around the web where your business is listed.
Search engines consider this data in deciding which businesses to show in geo-targeted results. They also use your NAP information across many websites, to confirm yours is a legitimate business. For example, businesses that don’t have an address on their website and have inconsistent info are seen as less trustworthy. Just like humans, search engines aim to recommend trustworthy businesses.
To make your life a little easier, Google in particular “normalises” some of the info in the NAP. This means you don’t have to fret about details such as Ste versus Suite and St versus Street. Check out this nifty article from Whitespark on what types of data Google normalizes: https://whitespark.ca/acceptable-google-maps-nap-abbreviations-and-variations/