Not-only-SQL "databases" are, along with HTML5, are basis for "next big thing" (or bubble) in technology...
While the first objective of non-relational those data systems is "horizontal scalability" to be able to handle very large amount of data by using commodity systems, along the way they also change way of thinking about the data storage and APIs.
Currently there is a wide variety of NoSQL databases, much more diverse than SQL DBs. But there is something common they share: there is "theory" behind distributed systems, similar to relational theory behind SQL databases.
CAP theorem can also help classify various NoSQL databases...
The CAP-Theorem postulates that only two of the three different aspects of scaling out are can be achieved fully at the same time