Starting by the obvious, what is a voxel ? A voxel is a short for volume element in the same way as pixel is a contraction of picture element. OK that doesn't really make sense but they just wanted to make it sound the same. There are different kind of voxels, one that we won't consider here is to see voxel as a way to represent volumetric object as three dimensional bitmaps instead of vectors (by opposition, polygonal objects are made of vectors). In this situation voxels are like Lego. Small bricks that constitute a bigger object, similar to the relation pixels have with the bigger image.

But here we'll only discuss the voxel terrain as featured in games like Outcast or Comanche. The voxel terrain engine is a 2.5D engine, it doesn't have all the levels of freedom that a regular 3D engine offers. It has the same degree of freedom as ray casting engines (popularized by Doom) and they are so close than in fact you could probably implement a voxel terrain engine as a ray caster. We won't do that, instead we'll use rasterization with a few tricks. Why is it called voxel if this isn't the same as the first definition ? Because our terrain is constituted by small 2D bricks that expand vertically. So this is a voxel, only a more restrictive definition of a voxel.