Yaoi is a popular term in anime and manga-fan circles. It means "boys' love" in Japanese. It is female-orientated anime or manga usually by female authors that is focused on homoerotic relationships and features idealised homosexual relationships. Since You guys can't tell the difference between shonen-ai and yaoi here is the main difference: shoen-ai is really graphic gay porn, considered hentai. Yaoi is as explained above. Yaoi themes pop up in anime/manga like Ouran High School Host Club and Hetalia Axis Powers but some "fangirls" find it in other shows/manga like Naruto or One Piece. The characters involved are usually beautiful teenage boys in their early to mid teens but in Hetalia Axis Powers, it is adults.
Yaoi is pretty much summed up by Hikaru and Kaoru's "forbidden brotherly love" act.