How does this illusion we call “reality” work? In other words, if quantum physics is  telling me this computer screen is nothing but a vibration, why is it that I see  this supposed solidity of the material? 

It is in fact an illusion that our five senses experience, which is then processed through the material reality filter know as the brain. Now, as we look at an object, which we now know is only a vibration, what actually happens is the translation of light.