There are a number of reasons why you’d want to re-mesh. One of the most common, is to combine multiple subtools into a single, unified mesh. Or you might do it for reasons of sculpting quality. Polygons, even at high subD level, can become stretched or distorted over time with repeated sculpting. Re-meshing redistributes and relaxes that surface geometry all over your model, so that the surface is smooth and sculptable again.
The reason he did it, as far as I can tell, was that he was near his systems max limit for polygons. When you subdivide, you multiply polygons by a factor of 4. Subdividing his existing mesh x4 would have produced a mesh in excess of his system limits (7 mil polygons in his case). So he was looking at 3million polygon mesh x4 = a 12 million polygon mesh.
So he remeshed creating a new base level mesh that was higher in polygon count than his original mesh, that when subdivided, produced a mesh that was somewhat higher in polycount at the highest level, but not over the limit. More polygons on a low level mesh can equal a few million extra polygons when subdivded, but still less than x4. His new mesh subdivided to 5 million polygons, a net gain of 2 million polygons, but still less than the 7 million limit.
Remeshing creates a new rough form based on your old mesh, appended to your subtool list. You can then apply Projection to it (ProjectAll), which transfers the fine detail from your old mesh to it, effectively letting you recreate the mesh , or combine multiple meshes, with new smooth, evenly distributed geometry over it for sculpting.
It is a somewhat more complicated version of the new Dynamesh process, that is still very useful, especially when working at high levels of subdivision, because dynamesh has practical limits in terms of polycounts.
