“What do nanometers measure?”

You can measure anything with length in nanometers.

The real question maybe should be ‘what do nanometers measure conveniently?’

For example, you could say your height in meters. You could also say it in nanometers.

But to say it in meters, probably gives you a number somewhere under 10. Which is a convenient number to think about.

You can measure something much longer in meters, say the distance from California to NY. But at that point, you’re talking about a very large number and it becomes more convenient to use kilometers since then you can use a smaller number of that unit.

With nanometers, it’s convenient for things like the wavelength of visible light and things at the atomic level.