Voxels are are used, like pixels are in 2D, in agglomeration to represent 3D (volumetric) forms. Voxels in the original sense in game development took two forms: "pure" 3D as seen in medical imaging applications, or heightmap based as seen in eg. the Comanche games and Ken Silverman's Voxlap engine. As such, these approaches to voxels used some sort of raycasting approach and so were not amenable to modern polygon rasterisation approaches. The more recent usage, such as that applied to MineCraft, refers to cubic polygons rendered using rasterisation approaches on the CPU or, increasingly, the GPU, as voxels.
A major benefit of Voxels is that they are amenable to real-time CSG operations, although the cost of reconstructing the voxel grid during such operations is often the primary limitation in implementing such systems.