The successful use of the scientific method depends on constructing clearly-stated, testable, falsifiable hypotheses. Assuming your hypothesis is correct, what should we expect to see? And what sorts of things should not happen if the hypothesis is correct?
Being testable is about being able to answer these questions. It has nothing to do with the truth value of the hypothesis. If a hypothesis is not testable, that doesn't imply that it's false.
Testability means that there is a way to settle a question based on evidence; there is a way to obtain evidence against an idea. If I claim that the moon is made of green cheese, that's testable. It's an idea that gives rise to predictions that we can operationalize (define in terms of concrete procedures and measurements) and test. Astronauts can collect samples; the samples can be analyzed for the presence of cheese.
But if I claim that the moon is inhabited by a supernatural, ethereal being -- one that can't be detected by our senses or by any technological device -- then my proposition is untestable. There are no observations we can make that would be inconsistent with my hypothesis. There is no test we can construct that has the potential to disconfirm my claim.
Does this mean that my hypothesis about the ethereal moon-dweller is false? No. It means only that the hypothesis is untestable, and, therefore, not a question that can be answered by the scientific method.
There are many questions or hypotheses that can't be answered by science because they are not testable. Some, like the moon-dweller hypothesis, are intrinsically not testable. What is the meaning of life? Will all creation be destroyed in the next century by an unknown, cosmic power? Is all reality merely the product of an elaborate dream? There seems no possible way to test these hypotheses, no matter what sort of technology we might develop in the future.
Other questions might be testable under certain conditions, but those conditions don't currently exist. They are not testable in practice. Such cases can help you appreciate the difference between being not testable and being false. In the 19th century, hypotheses about the composition of the moon were not testable. We lacked the technology to answer them. If someone back then proposed that the moon had rocks on its surface, there was no practical way to confirm or refute it. The hypothesis was, at that time, not testable. But it wasn't false.