Anime in general is characterized by a much higher art quality than traditional American animation, and much of the time contains more complex plots and storylines. The stories often deal with real life situations of death and love, emotion and emotional growth, presenting them in a mature and believable way not present in your average "saturday morning cartoons". In most western countries, cartoons are considered "kid stuff", but in Japan, the artists, voice actors, and production teams' names can be household words, well known and admired for the quality of their art.
Anime spans the breadth of genres. It is not just big robots on the rampage or little boys becoming gods. It is love stories, stories of swords and dragons, campy hilarious romps and almost anything else a person could want. Anime is all this and more!
Vocabulary
Anime - Rough translation of animation
Hentai - Pervert. Abnormality. Sexual perversion. Used also to describe a certain class of anime, manga or otaku (as in "H-Anime").
Japanimation - American term used for Japanese animation. Not to be used around die hard anime fans.
Otaku - Fan. Closer to fanatical. Not always a good thing.
OAV or OVA - Original art video or original video animation. Direct to video release, as opposed to being realeased to theaters or TV first.