Anime are basically (very basically) Japanese animation, commonly known as Japanamation (and a few other tasteless names we won't mention). But anime isn't just any kind of animation, anime is an art form. It's not uncommon to find adults watching anime or reading manga in Japanese subways and streets. Even in the U.S. adults tend to have a great interest in anime because of their complex plots. Because anime is considered an art form in Japan, the substance of the plot has more to it than two animals beating the crap out of each other. Their plots are usually highly developed, and their characters are realistically drawn and realistic psychologically. By realistically drawn I mean as real as people with hair in shade of the rainbow conceivable can be.. And.. if those people didn't jump 50 feet in the air.. And if they didn't go into their "super-deformed mode"... You get the picture ^_^. And because anime is so exclusively based on talent, it keeps people without talent (like me) from getting their crappy cartoons up on TV (maybe if I learn to trace better..). The amazingly striking art that composes anime can be strongly contrasted by that of American animation (cartoOns), which tend to be kinda dumpy.
So, what else is different and addictive about anime besides the characters, plots and kick-ass animation? It's something you sorta find out for yourself. With the wide variety of subjects that anime covers (from fantasy, comedy, romance and sci-fi to war, guns, secret agents and robots), it's almost impossible not to find at least ONE anime that interests you. Once you get into it, you're hooked. In the words of a wise, young Monkeyboy, "There's a big difference between some stupid, sucky Saturday morning cartoon and something kick-ass like 'Ghost in the Shell.'"
Term to Know: OAV ~ Original Animated Video
The Anime Page