When you hear anime the very first image to cross the mind will most likely be a graphic of little girls with skimpy clothing and huge eyes, or perhaps a teenage boy with unruly hair and super powers. While this is not only a wrong interpretation there's a lot more to anime than that.
In anime there are demographics that go over different target audiences. The ones with all the descriptions above are most likely to get shounen, that is basically anime targeted at boys. Then there exists the fluffy form of anime with princesses and magic, that is the shoujo demographic for anime geared towards girls. However there's two more demographics which can be often overlooked due to the fact that their target audience just isn't quite as mainstream since the two former - those two being seinen and josei. They are aimed towards boys in their twenties, respectively young women in their twenties and above, meaning that their geared towards a more mature audience.
Examples: Berserk can be a manga (and animated as anime as well), to utilize an example, published in the "Young Animal" magazine. It is really a magazine geared towards boys that contains a lot of violence and gore, and so it is really a seinen magazine.
นารูโตะ contains an intriguing plot about hardship and betrayal presented with a great deal of disturbing scenes involving rape and violence. NANA is a manga (and then an anime) serialized in the magazine "Kiss" which is aimed towards young women. The works published inside magazine often contain romance, intrigues, infidelity and heartbreak, and thus one can possibly conclude that it is often a josei magazine, since NANA contains several elements at the same time. To summarize: the very next time you hear the word anime, or simply being the vivid anime fan you're the the next occasion you look for anime to view, consider revising the picture you get in your mind. Consider that anime is really a medium, comparable to films or TV series, and thus inside the medium a myriad of expressions exist - both for younger and older audiences, for ladies and men etc.