The literal sense is a compound of 三 (san, “three”) + 枚 (mai, counter for flat things) + 目 (me, ordinal marker), literally “third sheet, third flat thing”...
【<span class="searchmatch">三枚目</span>】 [noun] Used other than figuratively or idiomatically: see 三, 枚, 目. (the third sheet or other flat thing) [noun] a comic character [noun] (by extension)...