Definition
A voxel combines "volume" and "pixel." It is one cell in a grid that divides 3D space like a checkerboard, and it is the smallest unit of volume that can hold values such as color or density. A voxel's position is not stored separately. It is set by which cell it is in the grid. Just as a flat photo is made of square dots, this technique shows a 3D object as a collection of tiny cube blocks.
A 3D World Stacked from LEGO Bricks
Coloring squares on graph paper to make a picture is called pixel art. A pixel is the smallest dot that makes up a screen. Pixel art is a flat picture with only a horizontal and a vertical position. Building a 3D statue by sticking clay or LEGO bricks together one cell at a time is what voxels are all about.
A computer screen is a flat, 2D surface. But the 3D game worlds we see have depth, front to back. A pixel only has a horizontal and vertical position. A voxel adds to that depth (front to back) information, making it a 3D cube.
Think of the world-famous game Minecraft. When you dig the ground and build a house, everything is broken into square blocks. Filling 3D space with a grid of equal-sized cubes to build objects is the classic picture of voxel technology.
Packed Full Inside vs. an Empty Shell
Most 3D games use polygons, the many-sided flat pieces that form the surface of a 3D object. Like a paper doll made of thin sheets of colored paper, a polygon model has only a surface and is an empty shell inside.
A voxel object, on the other hand, is packed with cube data all the way through. So when you slice an object with a knife or blow it up with a bomb, the cut surface and the broken pieces inside can look far more natural and realistic.
Thanks to this, voxels are very important in medicine too. CT (computed tomography) and MRI scans take thin layers of pictures of the inside of your body. Voxel data does the work when these many slice images are stacked up (in this case, voxels are often long boxes rather than perfect cubes) to rebuild the inside of an organ in precise 3D.
To Be More Precise: Why Isn't It Used Everywhere?
To be more precise, the more finely and smoothly voxels show reality, the heavier the load on the computer. Not just the surface of an object but also the invisible inside must all be handled as cube data, so computer memory and processing needs shoot up. Cut the side of each block in half, and you need 8 times as many blocks.
To show a curve or a round surface smoothly, you have to slice the blocks as fine as grains of sand. Then the number of blocks to compute swells to hundreds of billions, and an ordinary computer can hardly move the screen smoothly.
So modern computer graphics draws the look of things with lightweight polygons. It uses voxel technology in the right mix only for crumbling terrain, special effects like smoke and flames, and precise medical data.
Common misconceptions
Graphics made with voxels must always look blocky and angular, like Minecraft.
If you shrink the blocks to a microscopic size, the angular edges stop being noticeable and look like smooth curves. The only catch is a heavier load on the computer.
Where you meet it
A game world like Minecraft, where you break and stack cube blocks to build the world
CT and MRI scans at a hospital that let you look inside the body at organs and bones in 3D
In one sentence
A voxel is a unit of volume from dividing 3D space into a grid. It is a digital 3D block that can show both the outside and the inside of an object.