Peak power is the maximum amount of power that the speaker can handle over a short period of time before it fails. “Short” isn’t always actually defined, but we’re talking on the order of seconds or less.
RMS stands for “root mean square”, which is a type of average. RMS power is the highest *average* amount of power that the speaker can handle without failing. It can go higher than this for short periods of time (as long as it doesn’t exceed the peak power), but on average it needs to stay below this to keep working.
A speaker’s impedance (measured in ohms) is basically telling you how “heavy” of a load it is on the amplifier that’s driving it. Without getting into too much detail, we want to “match” the amplifier and speaker by ensuring that the speaker impedance is the same as what the amplifier is designed for. If you don’t do that (e.g. you have a 16 ohm speaker and an amplifier that’s designed for 8 ohms), the amplifier won’t be able to deliver all of the power to the speaker and you risk damaging the speaker and/or amplifier
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