The Split off Blocks function calculates the insertion of same-sized blocks of grid cells into the fragment. The size of these blocks is defined in the Volume Tools dialog. Grid cells which do not fit into those blocks are split off from the fragment. This makes sense when you want to insert a structure cell into the fragment which is bigger than the voxel size and does not fit into the shape of your fragment.
If you enter a blocksize X=3, Y=3, and Z=3, for example, all grid cells that do not fit into blocks of that size are split off and become a new fragment. If you leave the translations zero for all three axes, the calculation starts at the coordinates X=0, Y=0, Z=0. If you add a translation for one of the three axes, the insertion of the blocks will start offset from the zero coordinates.
If the Fill Incomplete Blocks check box is enabled, the grid cells that don't fit into the blocks are not split off. Instead, grid cells are added to the fragment to fill up the blocks, if no other fragments occupy the necessary grid cells.
If the Overwrite Grid Cells of other Fragments check box is enabled, other fragments, or parts of other fragments within the section of the new fragment, are overwritten.
Splitting off blocks can be very useful if you have structure cells with different sizes. For example, you can split off blocks in the size of the bigger structure cells to be sure that the structure cells will fit into the fragments.