Apache Hadoop is a Java framework that enables distributed processing of large datasets across computer clusters with a focus on scalability, reliability, and fault tolerance. It utilizes a MapReduce programming model to efficiently analyze data, exemplified by a case of determining the top student in each subject from a class of 50 students, which can be processed in a total of 75 minutes. The framework includes components like HDFS for data storage and YARN for resource management, facilitating various data analysis tasks.