Anime is, quite simply, animation -- cartoons. Anime is actually a Japanese transliteration of "animation". And hence, "anime" is Japanese animation.
But Japanese animation derives from Japanese "manga", which is Japanese comic books. These have dealt with topics that are anything but typical "cartoon" fare. Manga is as complete a communication form as the novel. Hence, manga has addressed the most adult of topics, and consequently anime has followed suit. Anime is not directed strictly at children or adolescents. I've seen anime which was seriously adult in its subject, and which evoked fully adult emotions and reactions. One of the most intensely emotional (read: depressing) films I've ever experienced was an anime movie called "Arcadia of My Youth". Never mind that it was animated; it hit you over the head like a sack of concrete in its raw presentation of the human dilemma. It was as powerful as any live action movie in presenting its message.
My point being that Japanese anime is not just "cartoons" as we in other parts of the world have come to know them. Anime is as legitimate an art form as live action movies, and can address and portray real-life issues as effectively as other mediums.