"Real" ground can mean a couple things:
There's "earth ground" which is a a connection that basically sends return currents to, literally, the ground, via a big metal rod, or metal plumbing, buried in the earth.
Then there's the "power ground", which is a safety mechanism that indirectly connects metal chassis to the earth ground, in case of an equipment failure that would energize it. That's where the third prong on your AC power cords goes. The neutral wire in your AC stuff is usually connected to this somewhere, and it's supposed to be pretty close (from a voltage perspective) to earth ground.
"Signal ground" is whatever your circuit is using as a reference for voltage. Since saying something has a voltage implies "between points A and B", the signal ground acts as a common point B for all the different point As you might have in your circuit. This often gets connected to power ground or earth ground somewhere along the line, and is usually created by the transformer. In a lot of cases it's the same thing as the negative power rail.
Audio electronics often need a dual power supply. Since single power supplies are often easier and cheaper, "virtual grounds" are basically a way of saying some point between the positive and negative power rail is going to be the new "0 volts" as far as the signal is concerned. This makes it look like you've got two pairs of power rails: the positive rail on the negative side is the negative rail on the positive side. That's basically what you're looking at with a dual power supply too, but here the difference is that the virtual ground is maintained by circuitry, instead of a physical ground connection. It's usually connected to signal ground.
And finally, some amps like the PPA use a ground channel with an active output; it keeps return currents from your headphones from getting back into the signal ground, and thus into the signal itself. Basically, the "output ground" is not really a ground at all, but your headphones can use it as one. Since it's the "output" of the ground channel circuitry, it should never be connected to anything other than the headphones or else you wind up with big problems.
Does all that seem logical? I hope it's not too oversimplified; it's one of those topics that you can usually get away without knowing a whole lot about but it's a really good idea to understand what's going on with it.
