Entropy is determined by how much information you need to fully describe the system. Very ordered systems require very little information to describe them. If you want to describe every atom in a crystal, all you need to do is describe where one atom is, and the structure and orientation of the crystal, and then you can figure out where every other atom is. If you want to describe where every atom in a living being, that takes a LOT of information.

Once common misconception that I see (I teach physics...) often in students is that when people describe entropy as disorder vs. order, they don't mean that it's randomness vs intricacy, what it means is that things that have regular patterns in them are low entropy and things with irregular arrangements have higher levels of entropy.