Many people say that anime is for 12-year-old dorks, but I myself have watched anime that would scar a 12-year-old for life. There is also shounen/ shoujo ai, which is gay/lesbian romance without sex, and yaoi/yuri, which is with sex. There is also Josei, for young women, which I imagine are like soap operas(Never watched any), and Seinen, for teenagers and young men, which are often horror or thriller animes, and are usually considered too scary for children. There are several different types, like Shounen, for boys, which typically feature a male protagonist and lots of fighting and action, Shoujo, for girls, with female protagonists and the main focus being romance or comedy. Often in anime, one episode will continue into the next, instead of each episode being a one-shot. There are always exceptions to these rules, such as in Hayao Miyazaki's movies, which have more realistic proportions and hair. Common elements in characters include large, shiny eyes, often spiky or unusually colored hair, long legs, etc. Anime is a form of animation orginating in Japan.
I hope to give a more accurate defintion that doesn't make me sound like an idiot. A lot of defintions on here for the word 'anime' have been hopelessly ill-informed.