‘Document-oriented database’ refers to databases that store their data in terms of documents. More specifically, structured documents and, by going with the times, documents in JSON (http://www.json.org/) format at that.
These databases belong to a category of databases called ‘NoSQL Databases’ (http://en.wikipedia.org/wiki/NoSQL). This category emerged over the last few years and in this blog site is used in that sense.
Databases that do not prescribe the content format or enforce a specific data model can store JSON by definition; so database systems that did not decide on a particular data representation upfront but left it open, can be considered document-oriented databases in case their payloads are documents.