NoSQL is a blanket term for the databases that solve the scalability issues which are common among relational databases. This term, in its modern meaning, was first coined by Eric Evans. It should not be confused with the database named NoSQL (http://www.strozzi.it/cgi-bin/CSA/tw7/I/en_US/nosql/Home%20Page). NoSQL solutions provide scalability and high availability, but may not guarantee ACID: atomicity, consistency, isolation, and durability in transactions. Many of the NoSQL solutions, including Cassandra, sit on the other extreme of ACID, named BASE, which stands for basically available, soft-state, eventual consistency.
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Wondering about where the name, NoSQL, came from? Read Eric Evans' blog at http://blog.sym-link.com/2009/10/30/nosql_whats_in_a_name.html.
In 2000, Eric Brewer (http://en.wikipedia.org/wiki/Eric_Brewer_%28scientist%29), in his keynote speech at the ACM Symposium, said, "A distributed system requiring always-on, highly-available operations...