Big data refers to datasets that are too large to be managed by traditional database tools. It is characterized by volume, velocity, and variety. Hadoop is an open-source software framework that allows distributed processing of large datasets across clusters of computers. It works by distributing storage across nodes as blocks and distributing computation via a MapReduce programming paradigm where nodes process data in parallel. Common uses of big data include analyzing social media, sensor data, and using machine learning on large datasets.