Mechanical Advantage is the ability to lift or move objects(load) with great output force while applying only a little input force. The trade-off is that you must operate the smaller input force for a large distance. This is all seen through the work Equation. Work equals force times distance (W = FS). As Energy is conserved, thus one can get a large force for a small distance equal to a small force for a large distance.
Mechanical advantage(MA) equals the distance of effort divided by the distance the object(load) moves. It is also equal to the output force divided by the input force.
The mechanical advantage of different simple machines like a lever, wedge, inclined plane, wheel & axle, etc. can be derived following the definition of the mechanical advantage given above. As the structure and operation of these machines vary, hence they have specific formulas for themselves. In the following section under “Related Study”, I have given links to 4 types of machines where you will get machine type-specific formulas of MA.