Connecting Flights at FRA

Please share what your layover time is. Anything more than two hours should be enough, but your parents may be more comfortable with longer. Is it all booked on one ticket?
I think by transit zone, they just mean going from one gate to the next.

IF your parents have a US passport (I'm assuming, since their trip originates in the US), and IF their flights are all on one ticket (they have the same booking number) then they won't need to go through Passport Control, and can stay airside (within the transit zone). Which means they can proceed to their next gate. Just follow the signs. The Frankfurt airport website is full of information. But the airport is huge, and this may require transferring to a different pier or terminal as well as possibltpy transferring to or from the plane by bus, so you need adequate time. What is your current connection time?

Where is the transit zone?

The transit zone consist of the top two floors of the A/Z building (the Z concourse), part of the B concourse, all of the C concourse, and part of the D/E concourse. They are the gates where out-of-Schengen flights arrive at FRA or flights to non-Schengen countries depart. As long as you stay in the transit zone, you don't need to go through immigration (Passport control), which you would need to do to enter the Schengen zone, i.e., Germany and the rest of Europe.

The transit zone was created so that people without visas for Germany (Schengen) could pass through FRA on the way to other non-Schengen countries.

The concourses, Z, B, C, D, & E, each have transit zone stations on the Skyline shuttle, by which you can travel between them. You travel in special "transit zone" cars which have doors that only open into the transit zones stations of each concourse.

What airlines are you using? Flights of the Star Alliance airlines (United, Lufthansa, et al) use A (in Schengen), B, and Z (out-of-Schengen). If you are flying on one or two of the Star Alliance airlines, there is a possibility that you will have to change concourses using the Skyline. If you are using non-Star-Alliance airlines (American, Delta, etc.), your transit will be made entirely inside the D/E concourse transit zone. If one, but not both, of your airlines is a Star-Alliance airline, you will have a longer connection on the Skyline Z or B to D/E or V.V.

Update: I combed the Internet and the FRA website looking for flights from Canada (Toronto?) and to Scotland (Edinburgh?), and I found flights from Toronto (both CA and LHA) arriving at Concourse B on the day I checked, and flights out to Edinburgh by Lufthansa leaving from Concourse B. So if those are your departure airport and arrival airport, you might be staying in the transit zone of the same building (Concourse B).

I've updated my original post with answers to the questions. Thank you all for your help!

As far as I can see, those two flights both use Concourse B, so as long as you get your boarding pass for the Toronto flight when you check in in Edinburgh, your entire stay in FRA should be in the transit zone of Concourse B.

If you don't get your boarding pass for the Toronto flight in Edinburgh, ask the flight attendant. You might be able to check in for the Toronto flight at the gate. You need a boarding pass in order to get through security into the concourse, but you'll already be there.