Tubes. archaic, obscure, 'shrouded in veils'. such terms as 'cathode bias', 'grid screens' and 'plate voltage' are a sampling of the commonly used, dense venacular; these terms mean something to someone... evidently, at some point in time, we learned how to make things loud via these little glass packages. i believe a bit background and a little history could be very enlightening.
so, where do tubes come from? how/why do they work? well the stage was set for the development of the vacuum tube with a number of incidents, here are a few:
-in the 1600's Robert Boyle's discovery of electro-magnetic forces in action across a vacuum. this had profound effects on theories over the propagation of electro-magnetic forces, but it also eventually lead people to discover that creating a 'perfect-vacuum' would create an environment free of charge particles that would interfere with an electron beam.
-Vacuum tube experiments with "cathode rays" (aka: electrons) start reaching the point of understanding (evidently, the better the vacuum, the more dramatic the effect). tubes like X-Ray tubes and Crooke's Tubes were being designed with greater understanding and for purposeful use. but by the late 1800's, an advanced understanding of even electrons was yet proposed.
-by 1900 we discovered what the electron was, and what it was doing flying around inside of vacuum tubes. thanks to guys like gauss, maxwell, faraday, volta, coulomb and many others, we had a pretty good 'classical' model, we had the math and experimental data to manipulate electron flow.
the ancestor of modern audio style vacuum tubes would have been called a 'cathode tube' back in the day. the tube would have come in various shapes, and would have had most of the air removed from it or may have even been filled with certain gases for experimentation. Two plates would have been set up on either side of the tube and voltage would be applied to the plates and causes a flow of electrons from one plate to another (cathode to anode). later a number of people (including edison) discovered thermionic emission, which produced a more steady and economical source of electrons.
up to ~1900, scientific aparatus was designed to explore the properties of everything electro-magnetic. along the way a quite a few devices were invented that benefited humanity greatly, but the stage was set for more intelligent design.
since electricity was already in use, certain needs became apparent. for example, AC current won the 'Current War' and long range transmission of electricity was now possible; but the need for a self contained rectification system became quite necessary since DC current was necessary in for widespread home use (rectification converts an AC current into a DC current). also, audio encoded onto a media and played back from and AC signal is already in use and the need for amplification of these weak signals was needed (this was necessary for both radio transmission, telephone/wire transmission, and disc/can audio media amplification)
armed with our more complete understanding of electro-magnetism, the first diode vacuum tube purposely built to allow flow of current in one direction, which became useful in the rectification process and in radio wave detection. it worked by passing an electrical current through a piece of filament until it reached it saturation point and thermionic emission was induced. these extra electrons around the fillament (the cathode) are then attracted to a [relatively] positively charged metal plate (the anode).
soon after the triode was invented because of the need for amplication devices. the device was very similar to the diode, but the added component of a 'grid' screen/electrode. the purpose of the grid component was sit between the cathode and anode so as to disrupt the electron flow between the components and effectively control the current passing between the cathode to anode. the controlling effect of the grid was acheived by running a current to the grid itself: as you alternate the current run to the grid you sympathetically divert the flow of the electrons from the cathode and divide them between the grid and the anode.
the HYDRAULIC ANALOGY link in the 'explanation of voltage, current and resistance' offers a great tanglble description of a triode.
the learning curve was brutal, progress was rapid. amplification was noisy and dirty. it broke alot too on account of the high plate voltages(tubes didn't even use emulsifiers back then!). for example, back in the day engineers didn't take into account 'biasing' the grid voltage on a tube and they'd get poor audio quality due to the fact that the tube nominally worked on the bottom of it's operational range and performance was not linear at such levels. later tube circuits would bias the tube to start operation closer to the center of it's 'linear' operating range so that you could get hi fidelity at even now volumes.
many such improvements were made, and people started adding electrodes while improving triode and diode design. so while people were dabbling with pin sets and optimization of triodes, engineers were also adding another couple 'grid' electrodes called a 'screen grid' and a 'suppressor grid' and soon pentode (5 electrode) tubes entered the market. around this time RCA started making tubes for commercial use (~1920)
we got more crafty, learned how to focus beams (beam tetrodes like the 6L6 in 1936), couple multiple tubes into 1 tube (like the dual triode 12AX7 is 2 triode tubes in one package ~1945)