Answer:
I think it can be explained by the fact that when you put salt into water, salt molecules NaCl divide themselves into ions : Na+ and Cl- . As they carry an electrical charge, they are put in motion by the electrical field created by the generator (a battery for example), thus a current can flow in salted water and it is said that salted water conducts electricity. It's a bit the same thing in metals for electrons, which carry a negative charge. Sugar molecules do not divide themselves into ions when they are put into water, they remain neutral, so they cannot participate to conduction.
Sugar is a molecular compound which in most cases cannot conduct electricity underwater. The salt is ionic so it can conduct electricity underwater.(Kind of like a summary)