Those are how big the microscopic circuit traces on the silicon chip are.
45nm uses smaller circuits than 65nm, i.e. 45nm is more miniaturized. Each circuit trace on the silicon trace is only 45 nanometers wide (that's 45 billionths of a meter).
The more miniaturized a circuit is, the less electrical power is needed to operate it, which means it runs faster and runs cooler (generates less waste heat).
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