Git is a version control system that allows developers to work together and track changes to files over time. GitHub is a web-based platform that uses Git version control and allows collaboration on projects. The speakers demonstrated how to set up Git locally, create a GitHub account, initialize and push a repository, make commits, create branches, pull and push changes, fork repositories, and make pull requests to contribute code back to the original project. Open source development was discussed, including competitions that promote contributions to open source projects.