Transformation of coordinates found in PDB
The purpose of these matrices is to reconstruct the crystal lattice from the coordinates, which only contain one copy of the repeating structural unit found in the crystal. In other words, they represent the affine transformations required to convert one copy of the repeating unit to its neighbors.
To a biologist (as opposed to a crystallographer), these are not useful except if one of the crystallographic symmetry axes happens to also be a biological dimer (or other multimer) axis. However, in this case, the PDB usually gives an option to download the &quot;biological unit&quot;, which includes the coordinates for all neighboring copies that associate in the cell with the copy specified by the original coordinates. I should point out that sometimes the biological unit is in fact smaller than the crystallographic unit, if multiple copies of a monomer or dimer or whatever occur in non-equivalent spatial contexts within the crystal. There is no substitute for biological knowledge to know what the relevant structural unit in the cell is.