The Pivotal eXtension Framework (PXF) allows SQL queries to access data stored in various data stores like HDFS, HBase, Hive, and others. PXF uses a pluggable architecture with components like a fragmenter, accessor, resolver, and analyzer that can be extended to connect to new data sources. It addresses the divide between SQL and MapReduce/Hive by enabling SQL queries to retrieve data without needing to copy it to the database first. PXF provides a single hop access to external data and fully parallel processing for high throughput queries across data stores.