The site that is top ranked by Google for the word NoSQL, nosql-database.org, has a definition:
Next Generation Databases mostly addressing some of the points: being non-relational, distributed, open-source and horizontally scalable.
Interestingly enough, there are cases where SQL databases have been used for Internet Scale sites. A good example is Instagram. In this posting, Instagram co-founder, Mike Krieger, explains how they used PostgreSQL scaled out to handle Instagram data. However, they had employ a lot of other NoSQL products like Memcache, Redis, and a fair amount of engineering to get it to work and handle the millions of users, creating content every day.
Due to it's success with Internet Scale projects, programmers have been using NoSQL for everything, and not necessarily with good results. I know on my recent projects we are starting to experiment with NoSQL to see if we get the speeds and optimizations that we need. However, I will not pretend that these projects are even approaching Internet Scale with may 150,000 users at best. However, after years of slow and complicated queries and indexes in SQL we do get the speed we need. Wish me luck.