How do waves relate to this?
留 means 'maintain' ; 'keep'; 'grew (of hair or beard)'
波浪 means 'wave'
式 means 'style'
发 means 'hair'

波浪式= wavy style
留波浪式发(型) = has wavy hair (style)

It is common to identify someone by something unique in his or her appearance, like hair styles, clothes color, etc.  when we don't know his or her name