Luigi is a workflow management system that allows users to build complex data pipelines. It provides tools to define dependencies between tasks, run workflows on Hadoop, and visualize data flows. The speaker describes how they developed Luigi at Spotify to manage thousands of Hadoop jobs run daily for music recommendations and other applications. Key features of Luigi include defining Python tasks, easy command line execution, automatic dependency resolution, and failure recovery through atomic file operations. The speaker demonstrates how Luigi can run multi-step workflows on the command line, including a music recommendation example involving feature extraction, model training, and evaluation.