Maven is a project management and build tool that promotes convention over configuration using a hierarchical Project Object Model (POM). It can build Flex projects by generating artifacts like SWF and SWC files. The flexmojos plugin supports Flex, AIR, and AS3 projects by adding goals for tasks like compiling, testing, documentation, and optimization. To set up a Flex project with Maven and flexmojos, developers use an archetype to generate the project structure, configure repositories and dependencies, then build and debug the project using Maven goals and phases.