Mercurial is a decentralized version control system with a simple design and high performance. It uses a graph model to represent the history of commits, with each commit having a unique identifier and references to its parent commits. Basic operations in Mercurial include checking out revisions, making commits on branches, and pulling/pushing changes between repositories to share work. Mercurial avoids problems like multiple branch heads through its branching model and by disallowing amendments to existing commits.