If there's no scientific way to prove that something's not true, it's unfalsifiable. You may believe that your dog dreams about rabbits, but since it's impossible to test whether he does or doesn't dream of bunnies, it's unfalsifiable.
A theory about something has to be falsifiable in order to be considered a scientific hypothesis. The statement "all cats are gray" is falsifiable, because you can observe many cats and prove that it's false. Unfalsifiable claims, which often pop up in conspiracy theories, can't be tested — it doesn't mean those beliefs are wrong, just that they're unscientific and impossible to prove.