I believe I just said nearly the same thing in the "What was your first anime?" thread, but oh well!
My best friend at the time was Japanese, and when were about 9 back in 1998 she introduced me to Pokemon and Detective Conan. They were on a VHS tape that she had, that a friend of hers from Japan sent every now and then. They had no subtitles, and so she'd have to tell me what was going on, but I liked the idea of them.
I knew they were weird Japanese cartoons, she tried explaining what Anime was to me, but I didn't understand it until I was about 13. I was real into Sailor Moon, Fushigi Yuugi, and Cardcaptors, and some friends in my class kept telling me "They're all anime, that's what anime is!".