Your question is to general, the maximum temperature of "a processor" depends on the processor, they are different depending on the processor. Mobile processors in laptops have higher max temperatures than desktop processors do, for example. Intel provides maximum temperature specs for their products which can be checked on their web site. Why the max temperature is a certain value is rather technical and really does not tell us anything useful regarding it's usage.
What information are you looking for?
How can I find out the max temperature for my processor? Some peoples tell that Tjmax in Intel specs is lower than processor can withstand, because the same mobile processors have 100 degrees Tjmax, so we shouldn't be afraid of temperature below it. The reason is that Tjmax is the temperature in the center of processor's case, but programs like Real Temp show us temperature from another sensors. And if processor takes temperature above Tjmax according to this progs, the temp of its case is lower Tjmax, so its really no reason for panic. Is it true?
Recently I've seen people, who told, that temperature below 100 degrees is quite tolerable for 45nm Core 2 Duos/Quads, and processor can hold out this temperature for everyday use (this temperature is reached under heavy load, of course). Will it degrade in a few month?