Hadoop is a software platform that enables the storage and processing of vast amounts of data using a distributed computing model, leveraging its core components like MapReduce and HDFS. It supports scalable, economical, and efficient data processing, capable of handling Petabytes across clusters and is designed with the assumption of hardware failure and batch processing. Various organizations, including Yahoo!, Amazon, and Facebook, utilize Hadoop for a variety of applications, demonstrating its effectiveness in handling large datasets and complex computations.