There are obviously many reasons, but to add a couple;

Fight regression

You don't want to fix the same bug several times, do you? When a bug is found, I first write a test to repeat the bug. Then I fix the code. Now every time I want to release a new version, that particular bug is tested yet again.

The 'quick fix' 5 minutes before launch

You're approaching deadline, everything is looking fine. Then, just before launch, a small bug or a tiny new feature has to be added. You can't imagine that would have side effects, can you? Well, that one bit of code, a small module that 'never changes', which you haven't looked at for 12+ months, reacts badly to this change. With good tests in place you catch this before you hit production problems.