A set of tests can prevent a bug making it out of the development environment, whether as the result of a change, or as a part of a new feature. This is especially important if several people are working on the same project.
Refactoring, or restructuring, existing code has a high chance of introducing bugs. If a script or function already has tests, the risk is reduced. Tests that verify the overall functionality (not necessarily unit tests) should continue to pass after refactoring.
To a degree, tests may also show how a piece of code is expected to work to someone reviewing or looking to contribute to the code.