What does "if it ain't broke, don't fix it" really mean?

I keep hearing and reading this nice proverb if it ain't broke, don't fix it. The latest appearance was in response to Shlomi Fish suggesting that some Ancient Perl code should be replaced by Modern Perl code.

I am not saying that every piece of code should be rewritten every 6 months but in my understanding that sentence actually translates to let's wait till it breaks and then panic.

I think people who say that sentence are afraid that the new version will break something. Sure there is always a chance that a change introduces an error but if we are afraid to touch the code what will happen when later on we encounter a case where it does not work? For example if we need to use it in a new environment. Will we have the courage to change the code then? How much will it cost in money, time, and lost sleep?

I think we have been trying to teach ourselves that we should have really good test coverage of our code and then we can easily refactor it and get rid of technical debt. So why do we keep hearing that sentence?