Ok Donr, I was worried you were going to 'earth-ground' one of the transformer wires.
Transformers have primary windings, where the input voltage is applied, and secondary windings which can increase or decrease the input voltage: 'Transforming'
the voltage to what you want. In your case 117VAC in/28VAC out. Most transformers have
at least the center-tap of the secondary. Which would be 14VAC, and it's there just
because it's useful in running other circuits in equipment. Although it's not always NEEDED, (and often not connected to anything).
depending on your machine.
'Grounding' the center-tap as of your transformer, means tying it to one of the other secondary
wires (NOT an earth ground). That means that even though you have a 28VAC secondary,
they're telling you to use it in the circuit at the 14VAC value of the centertap. Because
when you 'ground' the centertap, you're electrically 'short-circuiting', or disabling, half of the secondary winding output,
reducing the output voltage to 14VAC, instead of the 28VAC.
However: it sounds like your book is talking about electronics in general, and not in
reference to the machines specifically, that you bought. That directive, may not apply
to use in the machines you bought. When the manufacturer made your machines, they wired the circuit for what they needed. If you replace the transformer with the same
type, wire it the same way.
All these other smart guys have valid points about using technically correct terms when
discussing electronic topics, but you said you weren't a techno-nerd, so I'm trying
to speak in general terms.
Your confusion about the voltage you read on the transformer is because of the way
reading AC is done. You have to be tied to the actual AC ground of the circuit under test, the voltage almost
always reads higher out of an unloaded transformer than one connected to the circuit it
runs, and depending on how everything is connected, you can get some pretty wild
readings.
Anyway. Was your question just about the unexpected readings on your volt-meter,
or are you wondering about the replacement of your transformer?