Briefly it is the type of material including male x male romantic attraction. Stories with this genre focus on the character drama of the relationship. Shounen-ai is a Japanese term for "boy's love", while the term "yaoi" is used for more explicit, sexually focused material.
The word shoujo is a Japanese term for "young girl". This term is used for the section of the manga/anime market which is aimed at a female audience. Shoujo material tends to have a strong focus on interaction between characters, with a correspondingly reduced focus on action and global story.