There's an old saying that "the exception proves the rule." Many people get tripped up by this saying because they don't understand the context of the word "proves" in the statement. In this context, "prove" means "to test", as in "prove it". Stated another way, the saying becomes "the exception tests the rule." This is the essence of falsification.

Here's how it is supposed to work in science: Someone proposes a hypothesis to explain something. The hypothesis has to be testable. If the hypothesis fails a test, then it has been proven false (falsified) and must be revised to take into account the new data or be abandoned. This is where science differs from topics like religion where things are matters of faith instead of test and verification.

For the sake of simplicity, let's pick a historical example like relativity. People had noticed that under extreme conditions, Newtonian physics broke down and no longer accurately predicted what was being observed. Einstein proposed relativity as a means to better way to describe what was being observed. Over the years, relativity has been tested many times. So far, it has held up remarkably well. Suppose it fails a new test one day, what happens then? Well, after the test is verified, then the theory of relativity will have to be modified or replaced by a new theory that better explains what was observed. This is how science progresses.