When sodium chloride is dissolved in water, the water molecules surround the ions and separate them from each other. This process is called ionization. The ions are then free to move around in the water, and they can carry charge. This allows current to flow, and the solution is said to be an electrolyte.
The conductivity of a solution depends on the concentration of the electrolyte. The more concentrated the solution, the more ions there are to carry charge, and the higher the conductivity.