Automated tests are generally accepted as a best practice in software. They not only help us ensure our code is correctly implemented, but more importantly, they provide a safety net for future code changes or rewrites.
In the case of dynamic programming languages, such as Python, since there's no compilation step, syntax errors can go unnoticed. This makes it even more important to have unit tests going through as many lines of code as possible.
The two goals described can provide a guiding light when writing tests. The first goal for your tests should be to provide good test coverage; designing test cases that go through all your lines of code.
This alone will usually make good progress on the second goal—to show the functional correctness of the code—since after this, we will surely have a great starting point to build additional test cases for non-obvious use cases.