Chromium is the open-source version of Google Chrome.
Soon after releasing their Chrome web-browser, Google formed a group to release an open-source version to make it easier and faster for bugs to be fixed and features to be added. (Chromium does not include the auto-update functionality of Chrome.)
While Chromium was originally based on Chrome, now Chrome releases are based on stable Chromium builds. Chromium provides the latest features and bug-fixes (as well as new bugs and regressions) for users who want the bleeding-edge.