Hi John,
With a transformer the voltage relationship of the winding holds, so that you can apply the specified voltage to any winding and you will get the related specified voltage across all the other windings. Take an example of a mains transformer as follows:
(1) primary winding= 240V
(2) secondary winding #1=1V
(3) secondary winding #2=2V
(4) secondary winding #3=4V
(5) secondary winding #4=8V
(6) secondary winding #5=16V
Obviously if you apply 240V to the primary you will get the specified five secondary voltages in the normal way.
But you can also apply, say 1V, to secondary #1 (correction- thanks Les) and you will get the specified voltages on all the other windings, including 240V on the primary. In fact, you can make an inverter from a standard 12v + 12V secondary mains transformer. So, with some electronics, you can convert 12V DC (say from an automobile) battery into 240V AC.
You can also connect in series any, or all of the secondary windings, to give other voltages.
For example, if you connected all the secondaries together in series you would get a total voltage of 1V+2V+4V+8V+16V= 31V, or any other combination of windings.
In practice, there are a few factors to take into account because real transformers are not perfect, but the theory still holds.
spec