The trouble with describing logic puzzles is that it's impossible to make them sound as gripping as they often feel when you're playing them. In Oh! Cube's case, I thought I had a nifty get-out clause: I was going to link you to Eurogamer's review of Picross 3D, and say "it's basically this, but on your iPhone". Only Picross 3D was never reviewed within these pages, perhaps for the reason mentioned above. On, then, with the tedium!
The most common misunderstanding about Picross 3D is that it's Picross in 3D. Not so; it's Picross in reverse, really. Instead of using logic to gradually fill in squares in a grid, thus revealing a simple pixel image, you're removing cubes from a block, thus revealing a simple voxel object. In other words, it's not about what you leave in, but what you remove instead.
On the DS you'd chisel the cubes out with the stylus, but here you're using your finger. It's less satisfying, sure, but it's surprisingly difficult to tap out the wrong cube. That's partially because you have to give each one quite a sharp tap to remove it, which allows you to spin around your work-in-progress sculpture with your fingers without fear of cutting out a chunk in error.