There are many NoSQL solutions around, each one with its own strengths and weaknesses, so the following must be taken with a grain of salt.
But essentially, what many NoSQL databases do is rely on denormalization and try to optimize for the denormalized case. For instance, say you are reading a blog post together with its comments in a document-oriented database. Often, the comments will be saved together with the post itself. This means that it will be faster to retrieve all of them together, as they are stored in the same place and you do not have to perform a join.
Of course, you can do the same in SQL, and denormalizing is a common practice when one needs performance. It is just that many NoSQL solutions are engineered from the start to be always used this way. You then get the usual tradeoffs: for instance, adding a comment in the above example will be slower because you have to save the whole document with it. And once you have denormalized, you have to take care of preserving data integrity in your application.
Moreover, in many NoSQL solutions, it is impossible to do arbitrary joins, hence arbitrary queries. Some databases, like CouchDB, require you to think ahead of the queries you will need and prepare them inside the DB.
All in all, it boils down to expecting a denormalized schema and optimizing reads for that situation, and this works well for data that is not highly relational and that requires much more reads than writes.