I think of it as the professional version of iPhoto. I've used both. I use Aperture, but I am not a professional photographer.
What I've noticed so far in my use:
- Aperture gives you really great RAW capabilities, where the RAW image isn't rendered until you print or export. Which is nice because you can tweak white balance and such even after you've done other work to the picture.
- Editing is entirely non-destructive. Versions of picture can be managed much more efficiently than iPhoto.
- You have the ability to do projects and even folders of projects, which gives you more powerful organization features.
- Searching is more powerful
- Backup (Vaults) is easier to use, faster.
- All the keyboard shortcuts make working much faster for me
- Obviously you have a broader range of possible adjustments
- Metadata handling is much more sophisticated
- Stacks are a really cool feature, which make comparison between similar shots like brackets very easy. And keeps those more organized.
Again, a real pro will tell you more. But from a "prosumer" sort of perspective, that's what I like about aperture. The first two points are the reason I bought it.