the die is the actual processor. it is layers and layers of silicon doped with boron and phosphorus (or others). basically, if you dont know much about how this stuff works, you can think of the millions of transistors as tons of on/off switches. turning on the right ones can move the data around, multiply/divide/add/subtract, erase, or tons of other things.
the process size you hear about, i.e. 90nm, 65nm, etc., is the distance between nodes - lines of basically equal width and spacing. interestingly, the optics used to create the images can have a much bigger wavelength than what the process indicates. for example, the 80-90nm gate widths were created using ~250nm light (xrays).
edit: now that i think about it, this sort of smells like homework

if it is, you really should research it yourself since you will learn a lot. plus, it is interesting stuff.