A voxel is a pixel that managed to flee from flatland
A voxel is a value in a three-dimensional grid. A bit like a pixel in a image in a two-dimensional grid. Each voxel can contain a single piece of data, such as opacity or multiple pieces such as a color and material. A cell is a group of eight voxels that form a cube.
As voxels always is grid based the data set can get big fast. So splitting up it in grids for streaming is a good idea.
The common way to draw things is with triangles so surface extraction is used to get them. A number of algorithms for that are listed here.
For each cell take the voxel with the lowest coordinates and use it to set the material for the whole cell. Each cell is a box primitive with the the coordinates of the corners is the coordinates of each voxel in the cell. For cells that are made of solid material and is beside each other there is no need to create any face on that shared side of the cells. No one can see it as it is inside the wall.
This algorithm creates a more smooth surface. It works on a single cell at a time and classify each corner of the cell to be inside or outside the surface. That gives 256 possible combinations and that is used to select a layout of the triangles that exist in the cells. Cells where all the voxels generate no triangles at all.
Voxel terrain: physics - 2017
Voxel terrain: storage - 2017
Voxel Rendering Techniques - 2017
20 years of Voxel Engines - 2015
The Poor Man's Voxel Engine - 2015
Craft - 2014
Empirecraft - 2014
What is a solid? - 2012