Question : Problem: What does the "65 nm" in a 65 nm processor measure and is this independent of socket architecture?

Please explain if/how LGA775 (Socket T) boards can utilize 130nm, 90nm, 65nm processors and what the difference in the sizes represents.

Answer : Problem: What does the "65 nm" in a 65 nm processor measure and is this independent of socket architecture?

It describe the process used to create the processor. It means nothing but a die shrink. Doesn't necessarily means low power either. Some lower process even increase their power requirement, such as i7 and Pentium D. It has no other means. A die shrink means cheaper process, as they can cram their transistor into a smaller die.

You can think of it as a cake with choco chips. The smaller the choco chip, the more you can get with the same cut.

LGA775 refers to a socket where you put your processor. LGA775 can accept any CPU made with LGA775 type socket, the limiting factor is only its chipset.