"moving billow of water," 1526, from wave (v.), replacing M.E. waw, which is from O.E. wagian "to move to and fro" (cf. Old Saxon, Old High German wag, Old Frisian weg, Old Norse vagr "water in motion, wave, billow," Gothic wegs "tempest" see wag (v.)). The usual O.E. word for "moving billow of water" was yð. As for "billow", it is attested from 1552, from O.N. bylgja "a wave," from Proto-Germanic bulgjan, from Proto-Indo-European bhelgh- "to swell", or "to belly".
Etymology aside, I believe that what attracts me in waves is that they are the essence of everything a painting is not. They are never still. They are a continuous challenge composed of exquisitely fleeting instants. Every second is a provocation of sorts, a chaos theory conjugation of elements -- light, water, wind, current, shore -- that can never be properly captured.