Quick Intro to Tubes
A project such as this one can teach you a lot of about electricity and electronics. In order to appreciate what more or less goes on in this amplifier, we need to take a look at how a few things work, and first up are the vacuum tubes themselves.
A vacuum tube is just a glass tube that's had all the air sucked out of it. A good example is the early lightbulb, inside of which a filament was subjected to a current which caused it to produce energy in the form of light and heat. If the interior of the lightbulb were not a vacuum, the filament would experience combustion due to the high temperature in the presence of oxygen and be destroyed. The Diode
The most basic vacuum tube is a diode, so named because of the two electrodes which it contains. Vacuum tubes are said to be thermionic, meaning that heat is used to encourage the emission of electrons from an electrode. If a negatively charged electrode (as in it has an excess of electrons, in tubes it's called the cathode) is heated by a filament, the electrons in it become 'excited' and, if a sufficient electric potential difference or voltage is present, they will actually be emitted from the electrode. The potential difference is due to another electrode, called the anode or plate, which is positively charged and therefore exerts an attractive force on these enthusiastic little particles, causing them to whip across the vacuum from the negatively charged cathode. Since electric current flows from negative to positive and never the other way around, the current can only flow one way in a diode. However, this isn't much good for amplification, so let's move on to the next step in the vacuum tube hierarchy: the triode. The Triode
In a triode, there is a third electrode in addition to the anode and the cathode, called the grid. The grid carries a negative voltage and is connected to an input source, which, in the case of this amp, is a fluctuating audio signal. The negative voltage on the grid repels a certain amount of the electrons leaping off of the cathode, and how many electrons it repels depends on how negative it is, which in turn depends on the amplitude of the audio signal. This is by definition amplification: using a small amount of electricity to control a large amount. The audio signal is quite small, and it is effectively controlling the flow of however many electrons we choose to saturate the cathode with. The base voltage of the grid, the voltage that is present whether there is a signal or not, is referred to as the bias voltage. The bias determines how much current the tube draws when there is no input signal. The Tetrode
Add yet another electrode and you get a tetrode. This new electrode is called the screen or shield. Basically, the screen prevents the flow of electrons across the tube to be affected too much by the anode, and instead be totally controlled by the changes occurring in the grid. It has a smaller positive voltage than the anode. When the electrons initially break free from the cathode, they can only 'see' the screen, and so they rush towards it, and upon reaching it notice the anode and continue on towards that. The Pentode
Now we come to the pentode. In a pentode there is, obviously, a fifth electrode that wasn't there before. This is the suppressor. The suppressor sits between the anode and the screen and is somewhat negative in charge. Its purpose is to make sure any electrons that might bounce off the anode don't escape for too long by repelling them back into it.
Pentodes are not the end of the road when it comes to tubes, there are many other kinds, and if you're interested in them, check out the links step. There are two kinds of tubes used in this amp: triodes and tetrodes. The triodes are used in the preamplifier stage, where the audio signal is stepped up to a certain level suitable for further amplification by the tetrodes of the main amplifier.
Also, check out this fantastic old-fangled movie about tubes and how they are made: