Branch discovery configuration in Jenkins involves enabling a trait that scans the repository for all branches. Jenkins fetches the list of branches, applies any filters if configured, and then triggers builds for the selected branches. This process ensures Jenkins knows which branches exist and keeps the build process up to date. The execution flow starts with job setup, enabling branch discovery, scanning branches, filtering, listing branches, triggering builds, and ending the setup. Variables like branchesList and buildsTriggered track the discovered branches and how many builds start. Filters can limit which branches are built. Understanding these steps helps beginners see how Jenkins manages multiple branches automatically.