Happy to oblige, Jack! I've never fiddled with valve gear, but the principles are straightforward. As Mark stated, valves are great at dealing with high voltages, not so good at the current thing. So, unless you wish to go down the esoteric road of doing OTL circuits which I have never looked at, the way to get around this is to use a transformer, the big lump doing the output thing. If you didn't use one, you would blow the speaker and/or the valves because the impedance of the speaker would be too low!
Transformers, if good at their job, transmit power almost perfectly from the primary or input side to the secondary or output side, trading off voltage for current, or vice versa. Just like the mains or power transformer. A simple example: a 4 ohm speaker handling 16 watts means an 8 volts signal is being fed to it, 2 amps are flowing through it. So that the 16 watts power is being fed through the output transformer, in the shape at the output of 8 volts, 2 amps; 8 times 2 equals 16 watts. Assume the transformer is a 10:1 step down, which means that 8 volts on the output came from 80 volts on the input. But the power flowing through the input side of the transformer has to be the same (almost) as through the output. Simple arithmetic says that current on the input side is thus 16 watts divided by 80 volts, equals 0.2 amps -- 0.2 times 80 also equals 16 watts. As Mark said, a high voltage of 80 volts, a low current of 0.2 amps does the job in the valve area.
If you directly tried to feed that 80 volts into the 4 ohm speaker, that would mean 20 amps are flowing through the voice coil, and the speaker is handling 80 volts times 20 amps current, equals 1600 watts -- something's gotta give ...!!
The winding of wire in the output of the transformer has to be very low resistance, which means thick copper, otherwise it starts becoming a significant percentage of that 4 ohm speaker resistance, and power is lost in the transformer needlessly ...
Does that make sense, or am I explaining what you're after?
Frank