NoSQL databases are a type of DBMS designed to store large volumes of unstructured and semi-structured data with flexible data models, allowing for horizontal scalability and dynamic schema. They are utilized in various formats including key-value, document, column-family, and graph models, each offering unique advantages for specific use cases. Key benefits of NoSQL include high performance, flexibility, and often, eventual consistency, with trade-offs between consistency and availability as described by the CAP theorem.