SQL is not a database, it is a standard interface to a feature set commonly associated with relational models. Before everyone standardized on SQL, there were other relational query languages. The "No" part of "NoSQL" refers to the fact that some basic elements of relational implementations cannot be usefully expressed using a much simpler distributed hash table model.
All the "NoSQL" does is eliminate all the parts of traditional relational databases that do no scale -- discarding the bottleneck rather than fixing it. These are things like joins and external indexing. Unfortunately, discarding those things means you discard a lot of very important functionality as a practical matter, notably the ability to do fast, complex analytics. Adopting the NoSQL architecture runs contrary to the trend toward more real-time, contextual analytical processing. There are a great many analytical applications that are not amenable to batch-mode pattern-matching, and the NoSQL model is a lot less applicable than I think some people want to acknowledge. In its domain, it is a great tool but it has many, many prohibitive limits. We are essentially trading power for scale.
That said, do not take this as an endorsement of traditional SQL relational databases either, as they have a number of serious limitations themselves. As just mentioned, a number of the core analytical operations those models support are based on algorithms that scale poorly. The SQL language itself has mediocre support for many abstract data types (e.g. spatial) and data models (e.g. graph), which in part reflects the inadequacies of the assumed underlying database algorithms (e.g. B-trees) that are implicit in SQL. The inability to efficiently do event-driven/real-time applications is also more a reflection of the access methods used in databases than any intrinsic weakness in SQL; SQL may be clunky for that purpose, but that is not the real limiter.
A truly revolutionary deviation from SQL would usefully implement a superset of the features SQL supports, not take them away. Of course, we would need access methods more capable than hash tables and B-trees to useful implement those features, which is a lot more work than discarding features that scale poorly. NoSQL is a stopgap technical measure for that small subset of applications where the serious tradeoffs are acceptable.