The observation of a black swan falsifies the hypothesis “All swans are white”.
Here is an easy way to understand falsifiability. Suppose you say “It’s raining.” I then point out that cars aren’t using their wipers; people aren’t using their umbrellas; there are no puddles on the ground; nothing is wet; we can’t see water falling from the sky; etc. I have now clearly falsified your claim.
But if you respond “Well it’s invisible rain that doesn’t land on windshields or umbrellas or create puddles or make things wet,” then you have advanced a non-falsifiable hypothesis. Now let’s say, in an attempt to falsify this invisible rain hypothesis, I tell you that I have a special rain detector to detect invisible rain and it shows no invisible rain in the area. But still, you aren’t convinced and respond “well, my kind of rain can’t be detected even by such rain detectors.”
In this case what you originally meant by “it’s raining” isn’t what we ordinarily mean by that statement. You were referring to an invisible rain that you just believe in no matter what evidence I offer to the contrary—in other words, a non-falsifiable hypothesis. Not only is this absurd but note that your claim here that it’s raining is essentially empty or vacuous. Why?
Because you aren’t really saying anything when you say it’s raining. After all, what’s the difference between your idea of it’s raining and no rain at all? What we mean by the phrase “it’s raining” is that we see water falling from the sky, things get wet, etc. But if you say it’s raining doesn’t mean any of these things then again, what’s the difference between your rain and no rain at all? Of course, there is none. What you are saying is meaningless.
So if a hypothesis is in principle incapable of being falsified—no matter what evidence I produce—then that hypothesis or belief is just vacuous nonsense.
Let me give a different kind of example to make the same point. Suppose I believe bread rises in ovens because of the color of ovens. That may be a stupid hypothesis but it’s not empty; it can be falsified. All I have to do is put the bread in different color ovens and see if it rises or not. If it rises in different color ovens or only sometimes rises in the same color oven then I know the color of the oven has nothing to do with the bread rising. The “oven color” hypothesis is falsifiable. In fact, it can be easily falsified.
On the other hand, if I say invisible gremlins (whatever they are) cause bread to rise, and no matter what evidence you produce I continue to insist on the “gremlin hypothesis” then my hypothesis isn’t just falsifiable, it’s nonsense.
Now if you tell me its yeast that causes bread to rise and you put yeast in the bread and the bread rises and you take it out and the bread doesn’t rise and you do this over and over a million times then you have given me lots of evidence to support your”yeast hypothesis.” Now, it’s always possible it’s not the yeast (the problem of induction) but you have provided overwhelming evidence for the yeast hypothesis that a rational person should accept. And if I still claim invisible gremlins cause bread to rise after all this evidence then what I’m saying is just nonsense.
I’ll leave it to the reader to consider the implications of all this for beliefs in gods, devils, angels, miracles, the power of prayer, ridiculous conspiracy theories, etc. If you believe in such things, are your beliefs falsifiable? Would you allow anything to falsify your beliefs? If not, then your beliefs in such things are empty or vacuous. Believing in invisible gods, devils or angels may be just like believing in invisible rain or invisible gremlins. Such beliefs are not just false but essentially meaningless.
Here is a link to a more detailed and technical explanation of falsifiable and non-falsifiable beliefs or hypotheses.