Hadoop is an open-source software framework used for distributed storage and processing of large datasets across clusters of computers. It was designed to scale up from single servers to thousands of machines, with very large datasets. The core of Hadoop includes HDFS for storage and MapReduce for processing. Hadoop has seen widespread adoption by major companies for applications like advertisement targeting, security analysis, and more. Its advantages include low cost, fault tolerance, and ability to handle large amounts of data.