From Greek poly- ('many') + nēsos ('island') = 'many islands'. The Chinese transliteration uses pure phonetics:
波-
利-
尼-
西-
亚. Sister regions are
美拉尼西亚 (Melanesia, 'black islands') and
密克罗尼西亚 (Micronesia, 'small islands') — all share the
西亚 ('-nesia') ending.