ITRS defines process nodes based on the average size of part of a particular type of circuit. Specifically, a process is a "45nm" process if the transistors in a 6T SRAM cell are within a certain size range.
So, first, what's a 6T SRAM cell? SRAM is the type of memory used for caches on processors. One "cell" stores one bit of data, and it's called a "bit cell". The dominant circuit used for these cells nowadays has either 6 or 8 transistors (I'm not sure which is more common). Back when people walked to school, through 6 feet of snow, up hill both ways, the cells often contained just 4 transistors, but that style has become a very poor choice for a few reasons. The size of a bit cell is significant because there are millions of copies of the cell on modern processors, so any savings in the bit cell area translates to a good savings in the area of the whole chip. As it turns out, the way they're arranged on a chip is also very friendly to manufacturing, so they can use the very smallest sizes that can be made reliably. You could make a very over-simplified characterization of a process based on this property (this single number on its own really isn't useful for much more than marketing).
If you look at
this Intel 45nm SRAM cell, the horizontal shapes form transistor gates. The vertical dimension is referred to as the "gate length", and the distance from the top edge of one to the top edge of the next is referred to as the "poly pitch" (pitch = distance, poly = polysilicon = the material normally used for transistor gates). I think the ITRS definition of 45nm requires that this number is around 150nm (I can't find the exact number). If you look at the SRAM picture, note that the gate length isn't equal to the distance between two gates. The poly pitch is quite a bit larger than 2 gate lengths.
I labeled the Intel SRAM cell
here, but that's probably not very helpful for most people (we're seeing one layer too few for it to be clear).
Now, there are a few dimensions that people actually think of when they hear "45nm". The most common would be one of three things:
1) When drawing layout in a CAD program, the vertical dimension of the transistor gate shapes.
2) When that shape is actually printed, what the vertical dimension is.
3) The actual length of the path that the gate is controlling. Take a look at
this horrible drawing I made - the length of the path is just the part between the source and drain (labeled "Y"), and as you can see, it's less than the length of the gate (note that "length" is left-right in this picture; "width" would be perpendicular to the screen). By having the diffusions (the source and drain) extend underneath the gate, transistors can be made to perform better. I think this is the dimension usually referred to as "effective" length.
Corrections appreciated if I got anything wrong

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