Well, on the most basic level, Anime is Japanese for Animation. It refers to the styles of animation most prominent in Japan. It's also refered to hand in hand with manga, or Japanese comics.
Often times, series that will start out as manga will be transformed into an anime series. Some memorable examples of this would be Dragonball and Fushigi Yuugi.
When many americans think of animation, they think of disney movies, or the old Warner Brothers cartoons. In Japan, however, animation is a much more involved process. In Japan, there are levels of animation that run the gamut from children's programming to things much much more adult. The artistic styles and production techniques used are highly stylized and specialized.
There are three basic ways that anime is distributed in Japan; TV episoded, Original Video Animation, and full length feature films.
These are the animes that are aired on TV in Japan. TV series in Japan are run according to different syndication schedules/rules than in the US, and run very different lengths. Series such as Vision of Escaflowne, El Hazard:The Wanderers, or Tenchi Muyo! run only 26 episodes during the time they are on television, while other series such as Sailor Moon or Dragonball can air several hundred episodes. Many of the TV series are based off successful manga series, which provides lots of story material. The art in these anime range from fair to good, but since they allow more time for character development, they can be more enjoyable.
These anime are created for the big screen. Often they feature some of the best art work to be found in anime. They last generally anywhere from 60 minutes to 2 hours.
For more information about anime, go to the Links page in the pull down menu to the left of the screen