I really think for me, what it comes down to is animation with more adult themes. They aren't just your average cartoon. There are a lot of mature themes touched on by many animes that have this amazing ability of really transporting you to entirely new worlds. Some animes are dramatic, others are funny, and many of them can even be sad. Many of the animes I tend to watch have their own respective story to tell over the course of each episode, and I think are more relatable to many of the network TV shows than cartoons. The only different is they are animated, and a lot easier to produce because it is easier to animate than it is to use, say, CGI. It has its own style and method of delivering a story that is drastically different than a "cartoon" in my own opinion. While not everyone may like it, it really is an art and a genre of its own that is quite enjoyable - offering a little something for everyone considering just how many animes you could find.
~M