Peak power and my new CA speaker system

[Smokey]

I always wondered about this but what does total system peak power mean?

Peak Power is amount of headroom an amplifier have that can handle music peaks or spikes. It is more related to quality (distortion) than quantity (volume).

Like example my new Cyber Acoustics CA-3554 speaker system says 32 watts total RMS and 68 watts total system peak power. Does this mean that my speakers are technically has 68 watts of power? Or are they still 32 watts?

Your speakers have 32 watts of (usable) power. But you also can say speakers have 68 watts of power as long as power is labeled "Peak"

I heard that RMS means that the speaker actually have double the power like example if a speaker is only 15 watts RMS then it goes upto 30 watts total power.

Are you refering to speaker or amplifier power?

For amplifier, that statement is not correct. Without knowing Dynamic Headroom and THD (Total Harmonic Distortion) of amplifier, you can not make such an assumption.