Mechanical advantage is a measure of how much your force is multiplied, efficiency is a measure of how much of the work you do actually goes to moving the thing you're trying to move.
Consider a system of pulleys used to lift a heavy load: the pulleys provide a mechanical advantage to let you lift the load more easily, but in addition to moving the load, you also have to move the rope and the pulleys.
Adding more pulleys may increase the mechanical advantage, but it also increases the amount of extra stuff you're moving.
The more extra stuff you're moving, the less efficient the system.
