Why don't electrons dislodge with higher intensity? I understand that photo-electrons are not produced with increased intensity because frequency is what matters, however could someone give me a good intuition of why this is the case?
What exactly do electrons do when they are hit by photons? Why does intensity not matter, could you explain why in terms of what is happening in electrons\atoms which makes the intensity not dislodge a electron? 
 A: Einstein realized the answer to this question way back in 1905. In fact it was one of the most important theories in the dawn of the Quantum Mechanics revolution in physics.
Late 19th century physicists thought light was described completely as a wave which when continuously excited an electron for an amount of time would eventually eject it. However, this model failed to account for the immediate ejection of electrons that was observed. Light in the form of small packets or quanta might be able to eject an electron if it absorbed that energy all at once. This was Einsteins brilliant idea. He said that the energy required to eject an electron depends on the energy of a single photon being able to do the job. This of course depends on the energy of the photon or on the frequency as you stated. 
The intensity is of little consequence because if one photon cannot do the job then having several hit one after another who cannot do the job still won't get it done. Imagine a person trying to lift 300 pounds. If they are strong they can but if they are weak they can't. It doesn't mater how many weak people come along and try one at a time to lift it, the weight will never be lifted until a strong man A.K.A. a high energy photon comes along to do the trick. 
