MongoDB is a scalable, high-performance, open source NoSQL database

Formal description:

MongoDB - open source document-oriented database management system (DBMS), which does not require schema tables. Written in C++

In other words:

MongoDB is used to store, retrieve and update website data. Each file, without hard-coded scheme, may contain a collection of other files. This structure allows you to achieve high-speed read / write data, while still offering scalability.

What is it used for?

Use of MоngоDB would be highly encouraged for websites who's database can significantly increase over time. For example, where the website's content is generated by users. In this case, the resource would initially be empty, but over time, more and more data from users will be accumulated.