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2D is where during a cut the bit only travels in 2 directions (X and Y). The Z height stays at one depth for each pass. Profile and Pocket cuts generally. The Moulding toolpath in VCarve/Aspire lets you do limited 3D carving with multiple 2D passes.
2.5D is where the Z axis can move up and down dynamically during each pass. V-carving and fluting. Some 3D work is possible with clever application of the fluting toolpath.
3D is where all 3 axis move together to slowly carve a 3D shape. Small stepovers in X (or Y) axis. Z moves up and down while Y (or X) progresses through the wood.
4D is generally just a reference to using a rotary axis. You still may be limited to 3 directions of movement, although one will be rotational.

5D means 5 dynamic axis of movement for the bit during a cut. X Y and Z as usual, but add in rotation (tilting) of the cutting head in two axis. Permits cutting from the side around a 3D shape, and potentially undercutting which is impossible with only 3 axis.
 
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