Re-running earlier tests after every change to make sure what used to work was not broken by the new change.
Every change to software, even a small fix, can break something elsewhere with no obvious connection to it. That breakage is called a regression. Regression testing means running again the set of tests that passed before, to confirm they still pass. It does not look for bugs in the new feature; it guards the old ones.
The most embarrassing bugs are those that appear in something that has worked for months. And because repeating tests by hand is tedious, people skip it, which is why regression testing is the first thing worth automating. Fanann's QA Engineer re-tests after a fix and can be scheduled to run regularly without you having to remember. Practical tip: every time an important bug is fixed, add a test case for it to the permanent set. That way the same bug cannot come back twice without you knowing.