The NoSQL paradigm isn’t a way to work with a database without havinf to connect to a server. It is merely a term coined to reflect new “non-relational” models for organizing data, through a distributed architecture (it is not mandatory, though), and it should not be confoudend with the existing software NoSQL.
According to http://nosql-database.org/
, NoSQL is
Next Generation Databases mostly addressing some of the points: being non-relational, distributed, open-source and horizontal scalable.