The class of the amplifier relates to how many degrees of the output signal will be amplified. Figure what you are amplifying is a nice 360 degree sine wave in class A (see attached)the output tube (valve), transistor or FET will be conducting current for the complete waveform. Then you have class B that will only amplify 180 degrees or half of the waveform. Followed by class C for approx 120 degrees and then D for even less. A single ended amplifier can only drive current flow in one direction with tubes this is usually your common cathode circuit, transistors the common emitter and a FET is common source. As stated in the other posts you can parallel tubes or transistors for greater current flow and lower output impedance. A single ended amplifier could also be a class other then A you do not see this on guitar amplifiers but it is done on some subwoofer and maybe bass amplifiers. This is a bit of a special case because they are driving a tank circuit with an inductor and capacitor that will result in a full waveform being generated but with a limited frequency range.

Class A has low efficiency because the amplifier is always conducting so it is always dissipating power. Also it needs to be biased at the midpoint for maximum linear output signal so if it could do 100mA maximum it would be biased at say 50mA.
For class B the amplifier would be biased at cutoff so if it was the same amplifier (tube) as above it could drive the signal from 0mA to 100mA and with no signal in no power is dissipated.

In a two tube push pull amplifiers say the tubes are biased as class B and each tube can do a maximum of 100mA. One tube will be driven by the positive portion of the input signal by the phase splitter whilst the other is driven by the negative. Then you can provide 200mA peak to peak to the output transformer for 71mA RMS. Using the same tube in a class A amplifier would be 100mA peak to peak for 35mA RMS and being power is current squared times impedance the push pull amplifier would produce 4 times the power in this basic example.

However you do not bias right at cutoff in a push pull amplifier because this will cause crossover distortion so you have to waste some power at the no signal condition. Also do to the fact the tube is almost turned off half of the time (approx 50% duty cycle) the plate power is almost halved so you can drive the tube harder then in class A.

With push pull you have a split centre taped transformer with the plate supply at the center tap and a minimum of two tubes connected to the two remaining terminals of the transformer primary. The advantages of push pull are immunity to plate supply noise due to cancellation in primary windings. Lower output impedance due to output waveform driven on both positive and negative swing of input signal and lower harmonic distortion. Push pull operation can be Class A or various levels of Class AB on a guitar amplifier. There are subcategories of class AB relative to zero signal bias current in output tubes (relates to crossover distortion).

As a note for the single ended amplifier vs. the push pull relating to output impedance when the signal goes negative on the control grid of the single ended output the tube is being turned off at that point the plate supply, transformer primary inductance and reflected inductance are really driving things. While in a push pull one tube is turning off while the other is turning on hence lower output impedance for the push pull amplifier and lower distortion.

Another difference is transformer requirements due to the standing current in a single ended amplifier to prevent core saturation a larger transformer with an air gap is required for a single ended amplifier. On a push pull amplifier the zero signal current is low so a smaller transformer with no air gap can be used.