- What exactly is it?
On one hand, a specific system, but it has also become a generic word for a variety of new data storage backends that do not follow the relational DB model.
- How does it work?
Each of the systems labelled with the generic name works differently, but the basic idea is to offer better scalability and performance by using DB models that don't support all the functionality of a generic RDBMS, but still enough functionality to be useful. In a way it's like MySQL, which at one time lacked support for transactions but, exactly because of that, managed to outperform other DB systems. If you could write your app in a way that didn't require transactions, it was great.
- Why would it be better than using a SQL Database? And how much better is it?
It would be better when your site needs to scale so massively that the best RDBMS running on the best hardware you can afford and optimized as much as possible simply can't keep up with the load. How much better it is depends on the specific use case (lots of update activity combined with lots of joins is very hard on "traditional" RDBMSs) - could well be a factor of 1000 in extreme cases.
- Is the technology too new to start implementing yet or is it worth taking a look into?
Depends mainly on what you're trying to achieve. It's certainly mature enough to use. But few applications really need to scale that massively. For most, a traditional RDBMS is sufficient. However, with internet usage becoming more ubiquitous all the time, it's quite likely that applications that do will become more common (though probably not dominant).