A lot of things. Anime has taken advantage of the serial format moreso than any other type of animation around the world. They're not averse to espousing controversial philosophical visions. They experiment with different types of editing styles, pictorial compositions and narratives.
In many ways, anime is more for film-lovers than animation lovers. They aren't going to blow you away with how many fps they do or anything on the technical side. They're more about creating a vision, and finding different ways of telling stories. If you come to anime with the expectation of high production values or groundbreaking technical achievements, you're probably coming to the wrong place. But if you're coming to anime to find different themes, stories and/or personal expressions, then you may be pleasantly surprised at times.
(Even though there's also a lot of crap anime out there, especially today *grurablegrurable*)
Put it this way. Hollywood makes the most technically impressive movies in the world. They've got the SFX, the star power, and the resources to really make movies pop. But sometimes the odd viewer may crave something different than the machine-like creations of Hollywood. They stray outside and find movies with different voices. They look to indie films, or foreign films. They discover, say, Fuller or Godard or Bergman or Fassbinder and think, "well, this isn't as big and flashy and crowd pleasing as Hollywood, but it's certainly DIFFERENT!"
That's a bit like how anime is compared to say, animation in the west.