After watching3Blue1Brown's video, I get it. So I can share with you what confused me:
It's this part of the sentence: "average a bunch of points along that path". I know what averaging it, but I don't know what averaging "along a path" means. Also I was (wrongly) expecting the output of this function to be a real number - I just expect "energy" to be a number. Instead, here what we're doing is averaging complex numbers so the output is a complex number. What a complex energy means is left as an exercise to the reader.
Here's my suggestion for a sentence that would have worked better for me:
"To find the energy at a particular frequency, spin your signal around a circle at that frequency, and find the center of mass of the plot."
Presumably then we have to take the distance from the origin to get an amount of energy.