What charged particles make it possible for an electric current to flow through a solution of a salt in water(saltwater)?

In liquids, the charge carriers or particles are generally ions.

Ions are defined as an atom or group of atoms (molecules) that have gained or lost one or more of its valence electrons, giving it a net positive or negative electrical charge.

Ions carrying positive charge are called cations, whereas Ions carrying negative charge are called anions.

Distilled water is purified water that does not contain impurities so it does not conduct electricity, whereas the water we use in our houses (tap water), well water and pond water is not pure and contains lots of impurities which are generally dissolved salts, and hence conduct electricity.

Pure water (distilled water) is a bad or poor conductor of electricity, but when impurities (like salts) is dissolved in water, they form ions and these ions make it possible for an electric current to pass through the solution. This solution is known as electrolyte that contains chlorine and sodium ions that conducts electric current.