All 3D printers print in a series of 2D planes stacked up to form a 3D shape, never moving along the 3 axes at the same time.
In fact, it only moves in 1D (while moving upwards to start the next layer) or 2D (while printing in the same layer)...
On the other hand, non-planar 3D printing is based on 3D paths, which gives a much smoother 3D print.
Check the results yourself:
Don't think I should mention which is non-planar:
The slicer doesn't make 2D layers anymore, but 3D curves:
What do you think of it?