Around each ion is a cloud of nonzero net charge density of the opposite charge, as ions statistically repulse the like and attract the opposite charges.
When the external potential gradient is applied, the a ion and its "cloud" move in the opposite directions and the "cloud" effectively decreases the gradient for the moving ion. This causes decreasing the ion mobility and molar conductivity.
Another factor, decreasing the effective ion mobility and molar conductivity, is partial forming ionic pairs that are indifferent to the potential gradient. It occurs mainly for higher concentrations and/or for electrolytes with higher charges (like magnesium sulphate in sea water).
Replying the follow up question:
Different electrolytes have generally different $A$ parameter for the Kohlrausch equation. As both complementing ions are contributors to the molar conductivity, the electrolytes with the common ion have generally more similar coefficient values, compared to ones without a common ion.
The effects contributing to the $A$ value via the affecting ion mobility:
- Ions with higher mobility have bigger dynamic bias of their "anti ion cloud" leading to bigger $A$.
- Ions with bigger charge have stronger "ion clouds" and ionic pair formation tendency, leading to bigger $A$.
- Ions with bigger hydrated radius (note the opposite trend compared to naked ion radius) have weaker ion cloud", leading to bigger $A$. It correlates with the ion mobility.
The Kohlrausch law equation parameters may be found tabulated, or they can be determined experimentally from conductivity of solutions of different amount concentration.