According to Wikipedia, "Bishōnen, also transliterated bishounen, is a Japanese term literally meaning "beautiful youth." It describes an aesthetic widely shared in Asia—a young man whose beauty (and sexual appeal) transcends the boundary of sex....it breaks down stereotypes surrounding effete characters. These are often depicted with very strong martial arts abilities, sports talent, high intelligence, or comedic flair, traits that are usually assigned to the hero/protagonist...Some western anime and manga fans use the term to refer to any handsome male character regardless of age, or any homosexual character. In the original Japanese, however, "bishōnen" applies only to boys under 18...The slang word "bishie" is short for bishōnen, and is often used by 'fangirls': "Sephiroth is my bishie!!"
In lots of yaoi or shoenen-ai story - at least one of the guys (but frequently both) are bishies. But Bishōnen guys are in almost all anime/manga somewhere. They are supposed to be hot & somewhat feminine looking. (Not all posters here seem to get the definition.)