Conductivity changes with the concentration of the electrolyte. The number of ions per unit volume carrying the current decreases on dilution, so conductivity always decreases with a decrease in concentration.
However, molar conductivity increases with dilution. This is because the conductivity of a solution is the conductance of one unit volume of the solution, but molar conductivity is the conductance of that volume solution containing one mole of the electrolyte.
As the total volume of solution containing one mole of electrolyte increases, the decrease in conductivity due to dilution is more than compensated by an increase in its volume of solution that contains one mole of the electrolyte.