MongoDB is a NoSQL database that uses a document-oriented data model. It stores data in JSON-like documents within collections, rather than in tables as in relational databases. The document structure can vary from document to document, which makes MongoDB very flexible and useful for rapid application development. MapReduce is a programming paradigm that allows users to distribute computation across large datasets by mapping values to keys, and then reducing the values for each key. MongoDB supports MapReduce to perform distributed computations and aggregations on large datasets efficiently.