Continuous Integration (CI) in today's world essentially means every so often (per code commit, or several times a day, or daily, or whatever other frequency you like) the computer will automatically build the code and run a test suite on it if tests are written, while all the new code gets merged into the main branch. It has multiple advantages, like being able to catch breakage ASAP, and ensuring you don't introduce regressions or performance problems that you don't catch for a long time.

In short, it's a way for developers to not have to waste their time making sure everything works, because the system in place makes sure it works for them. That's especially handy in a team setting.