I'll start with the citation from a hypothetical conversation:
"This is being handled by Jonathan Swift."
— Who does he report through?
"He reports up through Jane Austen's org."
The Microspeak term report through (or report up through) comes up often in situations where people from different groups are working together. In its most literal meaning, to report through someone is to have that person as your manager, or your manager's manager, or your manager's manager's manager, etc. (Not that any of those people beyond two levels actually reads any of the reports you've written!)
Usually, when someone asks who a person reports through, they are looking for the manager who reports to an implied reference point. The location of this reference point varies depending context.
For example, if the discussion is in the context of coordinating efforts across all of Microsoft, then the implied reference point is Steve Ballmer. Somebody who works on Windows reports through Steve Sinofsky, whereas someone who works on Office reports through Kurt DelBene.
On the other hand, if the discussion is in the context of coordinating efforts within Windows, then the implied reference point is Steve Sinofsky. The answer to "Who does he report through" would be the manager who directly reports to Steve Sinofsky.
Bonus Microspeak: Org is a common short form of the word organization, meaning "group of people who all report (directly or indirectly) to the same person."