Molar conductivity and concentration
Kohlrausch in 1874 he demonstrated that an electrolyte has a definite and constant amount of electrical resistance. From 1875 to 1879, he examined numerous salt solutions, acids and solutions of other materials. This resulted in the law of the independent migration of ions, that is, each type of migrating ion has a specific electrical resistance no matter what its original molecular combination may have been.So this means that the electrical resistance of the ions in the solution that are migrating, and conductivity is just the inverse of this. 

CH3COOH which is a weak electrolyte, so does not dissociate completely. Since it's only the migrating ions that affect it, only the dissociated ions affect conductivity and specific electrical resistance no matter what its original molecular combination may have been.

At lower concentrations, since there are more water molecules for every CH3COOH molecule, more of these dissociate so there are more migrating ions meaning a larger conductivity. The molar conductivity is defined as the solution conductivity normalized by the total ionic concentration. So concentration increases without any significant increase in conductivity meaning the molar conductivity decreases rapidly.