A conductor is an object or type of material that allows the flow of charge (electrical current) in one or more directions. Materials made of metal are common electrical conductors. Electrical current is generated by the flow of negatively charged electrons, positively charged holes, and positive or negative ions in some cases. Can any other thing pass through ??
If the conductor is liquid (electrolyte), your hand could pass through it. Seawater isn't a very good electrolyte, but it's one you've probably touched. Ionic liquids are more conductive.
There are transparent conductors like indium tin oxide which light can pass through (the wavelengths may be restricted of course). ITO is used as an electrode on many flat screens.
If you dip one end of a wire in a cup of hot water and hold the other end, you'll feel that heat can pass through - or of course use a teaspoon. There's an overlap between electrical and thermal conductors which is fundamentally important to several areas of physics.
Sound can easily pass through conductors, arguably more easily than through air. Imagine sitting in a closed metal box: you'd expect to be able to hear what's going on outside. Or more prosaically set your phone playing some music, and wrap it in foil. You might want to use locally stored music, as the radio waves you need to stream will be significantly attenuated .