Anime is readily available to everyone (on the internet) and just seems to be getting popular these days. An actual reason why anime is liked worldwide? I guess different people have different opinions and I can't really generalise, but my guess would be that from the animation,to the plot, to the boobs there are tons of reasons why people could/ would like anime.
I feel my opinion on this matter is valid. Since I really dislike anime in general. What makes anime appealing is the storyline and the way it's graphically made, such as the gore, which is very hard to pull off the same way otherwise. It's a very emotive artform, sometimes it can also be a bit too much.
What I dislike is the excessive length to milk it. Kind of like the fast and the furious, we didn't need fucking seven of them. All of these things are what made E.g. Elfen Lied so good.