The Hadoop Distributed File System (HDFS) is the primary data storage system used by Hadoop applications. It employs a Master and Slave architecture with a NameNode that manages metadata and DataNodes that store data blocks. The NameNode tracks locations of data blocks and regulates access to files, while DataNodes store file blocks and manage read/write operations as directed by the NameNode. HDFS provides high-performance, scalable access to data across large Hadoop clusters.