A peak file is a small file (between 10kB and 20kB) where WavePlayer saves the waveform data of your audio files. This allows the players on your page to display a waveform much faster than it would do if it had to analyze the actual audio content every time a file is loaded.
WavePlayer also stores the peak files for remotely hosted audio files. In that case, instead of a simple peak file, it saves an info file that, in addition to the peak information, includes also all the ID3 tags extracted from the audio file during the analysis. This way, even when remotely hosted files are used, you can take advantage of instantaneous waveform rendering.