Anime is generally known as the Japanese form of animation/cartoons.

Manga is the Japanese word for comics.

Shōjo is anime and manga typically targeted at girls. Examples of Shojo anime are Sailor Moon, Full Moon, and Kalideo Star.

Shōnen is anime and manga typically targeted at boys. Examples of Shonen anime are DragonBall, Naruto, and Bleach.

Cosplay(costume play) is where people generally dress up as different anime characters. Here are some examples of cosplay (Deedlit, Kakashi, Chii)

Shōjo-ai means 'Girl love' in Japanese and generally focuses on femaleXfemale romances. An example of Shōjo-ai is Revolutionary Girl Utena.

Yuri is like Shōjo-ai but involves older female characters and more explicit sexual scenes.

Shōnen-ai means 'Boy love' in Japanese generally focuses on maleXmale romances. An example of Shōnen-ai is Descendants of Darkness.

Yaoi is like Shōnen-ai but involves older male characers and more explicit sexual scenes.