The vast majority of people think that science works with a pattern like "observe phenomenon, present hypothesis, prove the hypothesis correct with evidence and testing." Most people don't understand what scientists and other people are talking about when they say that a hypothesis must be falsifiable.
Falsifiability of a hypothesis is, in fact, even more important than how much positive evidence you have for it. And when we get down to it, much of hypothesis testing actually aims to show counter-proof of the hypothesis false, not proof of it as correct.
The thing is, a hypothesis can only be tested if there exist test results that would prove the hypothesis as false (or, at the very least, cast doubt on its veracity.) If there are no tests that could prove it false, the hypothesis is basically untestable. Thus these tests serve a dual role in a manner of speaking: Not only do they test the actual hypothesis, but also by their very nature (ie. being tests that try to disprove the hypothesis) they show that the hypothesis actually is testable in the first place.
If a hypothesis is not falsifiable, and therefore not actually testable, then it's not a very useful hypothesis because it cannot be corroborated as either true or false. This kind of hypothesis has no use in the real world because our understanding of the world does not change regardless of whether it's actually true or false. Such hypothesis has no practical applications.
Many people ask for proof of the existence of God (and others try to present it.) However, an even more relevant and important question would be: What kind of test could be used to actually prove that God does not exist? Which test result could be considered as strong evidence for his non-existence? In other words, is the God hypothesis falsifiable?
If you ask a believer "what kind of test result would convince you that God does not exist?" and if this believer is completely honest, he or she will ultimately admit that there is no such test. They will keep believing no matter what.