Before, when I thought of After Effects, the first thing that came to my head was an extra add-on for Adobe Premiere. F*ck that! AE is wicked powerful.
One of the coolest things about it is it's not actually 3D. It's more like 2.5D. You can do some REALLY amazing things with it that makes it look 3D... and in a sense, it is. Think of it this way:
Photoshop has layers to make up one 2D image. Well what if you were able to rotate those layers and give each of them a Z-axis? You could then create a cube. Cool. After Effects does exactly that + animation. You can even import a photoshop document and manipulate those layers. It's awesome!