Sawhorse projections generally show when something is antiperiplanar or synperiplanar, more easily than something like a Newman projection or a basic line structure can.
Take ethane as an example.
An antiperiplanar conformation has a #180^@# dihedral angle, i.e. the atoms of interest across one bond are on opposite sides along the vertical molecular plane.
A synperiplanar conformation has a #0^@# dihedral angle, i.e. the atoms of interest across one bond are on the same side along the vertical molecular plane.
A sawhorse projection approximates this 3D structure extremely well, and allows one to judge whether an #E2# reaction is likely to occur or not (it requires an antiperiplanar conformation).
A Newman projection would not depict the dihedral angle correctly, because one would be viewing the important atoms from the front instead of an aerial view.
Thus a #180^@# dihedral angle may very well look like a #120^@# dihedral angle, unless one knows the precise bond lengths of interest to recognize when the bonds are not entirely opposite to each other.