The peak power handling value refers to the maximum power level that the speaker is capable of utilizing in short bursts. For example, a speaker with a 30W RMS rating but a peak rating of 60W means that speaker can comfortably run with 30 Watts of continuous power, with occasional bursts of up to 60W.
Peak power is always higher than RMS power, due to the fact that audio signals vary greatly and sometimes a spike in the audio level will occur. Peak power is the amount of power a speaker can handle without being blown or malfunctioning. This will cause distortion briefly if it is a spike in the signal level sent. Similarly running on peak power continuously will damage a speaker.