Why is simple: When you dissolve more of any salt that ionizes in water, there are more ions to "shuttle" energy carrying electrons across at a time. How is a bit more complicated. You see when you dissolve a salt in water, the molecules, due to some phenomenon, dissociates and each atom is charged either positively or negatively due to less or more electrons respectively. When you insert two electrodes in the solution to complete a circuit, the anode terminal is positively charged due to holes concentration, and cathode terminal negatively charged due to electrons concentration. The anode attracts the negatively charged anions and on contact with the anode, they loose electron(s) to the electrode. Likewise the cathode attracts positively charged cathions, and they gain electron(s) on contact with the electrode. The atoms become their neutral self as they drift away from the electrodes. These atoms, due to the inherent cahotic random motion at the atomic scale, collide, bond, and ionize almost simultaneously and instantaneously to restart the cycle again.
Now the more of these ions available to transport electrons and also create a dense cluster of themselves increasing the chance of quicker collision to restart the cycle, the more conductive or less resistant a salt solution is. The above explained process explains why a warmer solution is to some degree more conductive than a cooler one, because the increased kinetic energy in the solution helps increase the frequency of collision of neutral atoms.