Think about this in a really basic way. You're adding some mass to a beaker of water, right? Adding mass means that to raise the temperature of this solution we now have to add more energy in (via heat flow) than we would if we had less mass. The pure water has less mass than the pure water + salt, so the heat capacity of the solution is greater than that of the solvent alone. For the next point bear in mind that the salt solution also has greater volume than the solvent alone.
The confusion here is that when comparing equal volumes of solutions, say exactly 1.00L of pure water and 1.00L of 20% salt solution, the salt solution has a lower heat capacity. In its dissociated state, salt has a lower heat capacity than water, so by replacing a portion of the mass of the pure water solution with an equal amount of something with a lower heat capacity, we end up with a lower heat capacity of the 20% salt solution in comparison to the pure water.