Real power is RMS (Root Mean Square) while PMPO means music power (Peak Music Power Output). To compare those – you need to split PMPO by 3. You will then get RMS (almost! not exactly). For example if you have a speaker with 19W RMS / 50W PMPO.
RMS is a voltage that is put to the speaker in a constance way, without damage to sound quality or speakers. PMPO is the highest power at the highest voltage to the speaker that lasts less than second.
PMPO is a marketing symbol, because it’s much nicer for producers to put some big numbers. So to be honest, PMPO was created for cheating people at the shops.
When we speak about amplifiers, it is power that amplifiers can produce at all time, without any damage.
There is also some comparrisson with voltages. If the effective value is 220V, and 310 is the maximum (311V) it is because maximum value = effective * the square root. You can very easily check that by testing the current by multimeter and then check at the oscilloscope. You will see that measurement instrument will show 220 while the amplitude of current at oscilloscope is 310.
How we can use that in practice way. In general the speaker power is split by 2 (or3) and we get the amplifier, for example: if we have a 100 watts speaker, we can plug it to amplifier with power output about 50watts. Of course we can plug stronger speakers but not too strong.