Shonen, or "shounen", anime and manga are created for and marketed to boys. These stories have more action and fighting than other types of manga and anime. They typically feature male protagonists who may or may not have a love interest. They are often (but not always) fast-paced and focus less on plot and more on action. In addition to fighting-style shonen, there are stories centered on sports and romantic comedy.
Shojo anime and manga are stories aimed at the teenage girl market. They often, but not always, feature main characters who are teen girls with magical powers, a subset of shojo called "maho shojo," which means "magical girl." Shojo manga and anime focus on character and relationship development, even in the stories with action elements.
Yuri anime and manga revolve around romantic love between women. The lesbian themes may be sexual, emotional or both. This type of manga and anime is sometimes referred to by Americans as "shoujo-ai," or "girl love." The website Yuricon defines three types of yuri: written by men for men, written by women for women and written for lesbians by lesbians.
Yaoi is the Western term for what is more properly called "shounen-ai," or "boy love." This genre of anime and manga details the romantic and emotional entanglements between gay men. Many of yaoi's devoted fans are girls and women who enjoy reading about the idealized love between "bishonen," or "beautiful boys," though the genre's explosion of popularity in the Western world is argument that there is a wide, non-gender-specific audience for these stories.