Why? Because consistency in your name, address and phone number increases Google‘s confidence that it has correctly understood who, and where, you are.
Initially applicable only to local businesses and local SEO, the concept has become important for all businesses. With entity-based search (the switch from strings to things, as Google puts it) and the increasing importance of the Knowledge Graph, consistency of information about a business across the web has become absolutely essential to SEO strategy.
NAP is more than Name Address Phone
Initially for local SEO, the focus was on this simple triumvirate. However, consistency across the web for all information about a business, or indeed any entity, now often falls under this term.