You change the position and identity of the atoms in your model until there is very little residual electron density left remaining.

These are words, but I don't see how they prove the model. I guess it's like some sort of check after the operation is complete?

Why does a low residual electron density prove the model? What is electron density anyway? And how do we measure it?

Yes humans communicate using "words". Nothing is ever "proven" in science since there is always an arbitrarily complex hypothesis than can explain captured data. Instead, the weight of evidence is considered.

Anyway it seems like this whole conversation is out of your depth currently. There are many good X-ray crystallography texts available if your interest continues.