What does "Per John:" mean?
From the context of the article I'm reading (article unlinked), it seems to mean "From John:" or "John (said):"
What exactly does the word "per" mean when used as such?
"Per" in this case means "according to", taken from the Latin word per which meant "per : (+ acc.) (cause) because of, on account of. "
The OED has a citation from 1818 where the meaning is "as laid down by (by a judge)"
Well, there's another very important usage of this word, one that hasn't been mentioned yet.
In this case, per has a meaning for for each. This matches with the main question as asked in the topic title, but doesn't with the example given in the thread itself: per John, as you never charge something per John, haha.
There's another case where per would fit both your examples. Like this:
Which basically means you finished the job as John ordered you to.