The important characteristic of the isolated side of an isolation transformer is that the whole winding is completely isolated from everything.
Voltage appears across the winding, i.e. between the Phase and Neutral inputs to the powered appliance, but this supply is fully floating relative to everything else.
It's like the AC version of a battery. Imagine you're holding a 1.5V battery in your hand. You would measure 1.5V if you connected your voltmeter straight across the battery, but if you measure voltage from either terminal of the battery relative to some other point - the ground outside, for example - you won't measure any voltage, because the battery is fully isolated.
This is what they're trying to convey in the diagram by showing "0V" between each side of the isolated winding and earth. They're showing that if you measure voltage between those points, ideally, you won't get a reading.
That diagram causes confusion because it's not possible to measure those three voltages, as marked, simultaneously. The two measurement connections that are marked "0V" will only show 0V if measured separately. If you measure them simultaneously, using two multimeters, they will not (cannot) both measure 0V simultaneously.
Even if you measure them independently, as Steve pointed out, in real life you will probably measure some voltage between each side of the secondary and ground, especially if you use a voltmeter with high input impedance, because of leakage and coupling.
Down here, at least, isolating transformers must not have any connection to the earth pin on the isolated output socket. I can't explain why the ground is shown connected all the way through. Here, that would be illegal.