Q:

What does AGPLv3.0 section 7f mean and can you give an example of its use? 

In section 7 of the AGPLv3.0 there is the possibility to make limited changes to the license. 
I don't think I understand the changes allowed by subsection f) and I have certainly never seen it applied.  It seems to me like it allows someone to not just ask money in exchange for the program, but also to ask money from all downstream recipients of the program, in essence creating a program that is free as in free software, but not gratis. 
I always understood the "not-gratis" clause to be kind of a technicality, because it only applies to the first distribution and redistribution need not be indemnified.  But this seems to create the possibility for free software that is truly not gratis. 
Right?  And can you give an example of this clause's use, if a significant one exists? 
I quote section 7 below, with irrelevant subsections omitted:

Additional Terms. 
"Additional permissions" are terms that supplement the terms of this
  License by making exceptions from one or more of its conditions. 
  Additional permissions that are applicable to the entire Program shall
  be treated as though they were included in this License, to the extent
  that they are valid under applicable law.   If additional permissions
  apply only to part of the Program, that part may be used separately
  under those permissions, but the entire Program remains governed by
  this License without regard to the additional permissions. 
When you convey a copy of a covered work, you may at your option
  remove any additional permissions from that copy, or from any part of
  it.   (Additional permissions may be written to require their own
  removal in certain cases when you modify the work.)   You may place
  additional permissions on material, added by you to a covered work,
  for which you have or can give appropriate copyright permission. 
Notwithstanding any other provision of this License, for material
  you add to a covered work, you may (if authorized by the copyright
  holders of that material) supplement the terms of this License with
  terms:
[sections a to e omitted]
f) Requiring indemnification of licensors and authors of that
  material by anyone who conveys the material (or modified versions of
  it) with contractual assumptions of liability to the recipient, for
  any liability that these contractual assumptions directly impose on
  those licensors and authors. 
All other non-permissive additional terms are considered "further
  restrictions" within the meaning of section 10.   If the Program as you
  received it, or any part of it, contains a notice stating that it is
  governed by this License along with a term that is a further
  restriction, you may remove that term.   If a license document contains
  a further restriction but permits relicensing or conveying under this
  License, you may add to a covered work material governed by the terms
  of that license document, provided that the further restriction does
  not survive such relicensing or conveying. 
If you add terms to a covered work in accord with this section, you
  must place, in the relevant source files, a statement of the
  additional terms that apply to those files, or a notice indicating
  where to find the applicable terms. 
Additional terms, permissive or non-permissive, may be stated in the
  form of a separately written license, or stated as exceptions; the
  above requirements apply either way. 

A:

I'm fairly sure I know what it means, but I have as yet no examples of its use.   I think it's designed for use cases along the lines of Cygnus, where a company distributes another party's (A)GPLv3 code to customers who are paying for a support contract, or for some other assumption of responsibility, for issues with the code. 
Such parties as Cygnus are "convey[ing] the material ... with contractual assumptions of liability to the recipient".   If the original author chooses to distribute with clause 7f active, then any second party who uses the code in this way is required to include in those contracts "indemnification of licensors and authors of that material".   Given all the disclaimers in the (A)GPL, I don't think any sane party would for a moment assume that any liability attached to the original author, but 7f requires this to be made explicit to paying end-users. 
In concrete terms, suppose Alice writes program foo and distributes it under (A)GPLv3.   Bob downloads it and packages it, and offers it for a fee to Charlie under the terms of (A)GPLv3, along with a contract that says that if Charlie is using it and it breaks in the next year, Bob will fix it.   Clause 7f allows Alice to require that such a contract explicitly state that both Bob and Charlie agree that Alice is in no way responsible if it breaks, and nor is anyone else in the supply chain, except Bob. 

it allows someone to not just ask money in exchange for the program, but also to ask money from all downstream recipients of the program,

I don't read it that way, and I've never met anyone who thinks you can do that.   The (A)GPL is very clear that downstream recipients have to get the same rights that you have.