What does it actually mean to debunk something

A logical argument is one in which if all conditions are true, the conclusion must also be true. If any case can be made that the conclusion can be false in any case where all the conditions are true, then the argument is bad.

An example of a good argument is:
All well formed cats have toes
Mark is a well formed cat
Therefore Mark has toes.

If, in the example above, there is any case that could be argued in which Mark does not have toes, either Mark is not a well formed cat, or not all well formed cats have toes. Proving this disconnect is what debunking is all about. Fallacies are patterns of argument that are logically flawed and thus defeatable in an argument. Knowing common fallacies helps you pick out these known failing arguments and attack them.

Unfortunately, in today's world, almost no one argues logically and makers of fallacious arguments tend to jump from one to the next, even changing the baseline argument to avoid appearing to have lost an argument. So modern internet arguing usually uses the term "Debunk" to mean that someone else made a statement, true or false, that fits nicely with the predetermined conclusion of the arguer. They think as long as they are on the attack with statements, true or false, and you are stuck trying to build a new argument to show them why they are wrong, they are winning.

When one party does not argue in good faith, does not recognize when facts are against them, and cannot even accept a fact if it goes against their articles of faith in politics, there is no way to have a fair argument. Recognize early on that the person you are arguing is arguing to be right, not to teach or reach the truth, and therefore you are wasting your time.

I think I'd rather spend a night in jail for hitting them rather than debating them.