This week's book giveaway is in the OCAJP 8 forum. We're giving away four copies of OCA Java SE 8 Programmer I Study Guide and have Edward Finegan & Robert Liguori on-line! See this thread for details.
MongoDB is one of the databases that people mention as being well-suited for "big data," though scaling is always a tricky thing to do right.
Since MongoDB does provide a fairly straightforward way to do sharding (partitioning) of your data across many physical servers, it tends to scale well horizontally. So if your data can be partitioned that way, MongoDB is possibly a good fit.
So in summary, yes, it scales well to big data, though maybe not as well as something like Apache Hadoop (though it is a good bit easier to use than Hadoop).