The octree is used by mmg3d to partition the mesh vertices and thus, to speed up the vertices insertions.
During the insertion step, we don’t want to insert a vertex to close from another one. Thus, before inserting a point, we seek the octree cell to which the new point will belonging and we check if it is not too close from another point of this cell or of one of the neighbouring cells.
By default, an octree cell may contain at most 64 vertices, then it is split into cells (with d the mesh dimension).
You can use the -octree option to modify the maximal number of vertices per octree cell or to disable the octree (-octree -1).