Uses of NoSQL database in data science
To be perfectly honest, most NoSQL databases are not very well suited to applications in big data. For the vast majority of all big data applications, the performance of MongoDB compared to a relational database like MySQL is significantly is poor enough to warrant staying away from something like MongoDB entirely.

With that said, there are a couple of really useful properties of NoSQL databases that certainly work in your favor when you're working with large data sets, though the chance of those benefits outweighing the generally poor performance of NoSQL compared to SQL for read-intensive operations (most similar to typical big data use cases) is low.


No Schema - If you're working with a lot of unstructured data, it might be hard to actually decide on and rigidly apply a schema. NoSQL databases in general are very supporting of this, and will allow you to insert schema-less documents on the fly, which is certainly not something an SQL database will support.
JSON - If you happen to be working with JSON-style documents instead of with CSV files, then you'll see a lot of advantage in using something like MongoDB for a database-layer. Generally the workflow savings don't outweigh the increased query-times though.
Ease of Use - I'm not saying that SQL databases are always hard to use, or that Cassandra is the easiest thing in the world to set up, but in general NoSQL databases are easier to set up and use than SQL databases. MongoDB is a particularly strong example of this, known for being one of the easiest database layers to use (outside of SQLite). SQL also deals with a lot of normalization and there's a large legacy of SQL best practices that just generally bogs down the development process.


Personally I might suggest you also check out graph databases such as Neo4j that show really good performance for certain types of queries if you're looking into picking out a backend for your data science applications.