Mechanical Efficiency relates to the amount of Force lost in a mechanical process. It's different than electrical efficiency as in cellphones.

A good example is a bicycle. Look up some equations on "Mechanical Advantage" in a physics textbook. They usually have bicycles in their equations for gear ratios.

Mechanical Efficiency is basically a measurement of how much Force is lost in a mechanical process, like I stated before. For example, with a bicycle:

You put 100 foot pounds of Force onto a pedal. That pedal drives a gear, which drives a chain, which drives another gear, which drives the rear wheel. At every point, you have Friction. So let's say for example that at every point in the process, you lose 3% of your original Force that you put in. So from the pedal to the gear, you lose 3% from the bending of the metal, and the elasticity of your foot and shoe. Your efficiency is at 97% and your Force is down to 97 foot pounds. From the gear to the chain you lose another 3% from the stretching of the chain, so your efficiency drops to 94% and your Force is down to 94 foot pounds. From the chain to the rear gear you lose another 3% due to the bending of the chain and the bending of the derailleur. So your efficiency is now at 91%, and your Force is at 91 foot pounds. And from the rear gear to the rear wheel you lose 3% from the bending between the gear and the rear wheel. Now your efficiency is down to 88%, and your Force is at 88 foot pounds. From the rear wheel to the road you lose 8% efficiency because of the bending of the spokes, and the bending of the tire. So now the final efficiency of the bicycle is down to 80% and your Force is down to 80 foot pounds. You went from 100 foot pounds at the foot to 80 foot pounds at the road, because of all the friction and bending involved in getting the power from one place to another.

There are many other examples of mechanical efficiency, but that's the best one I can think of right now.

Should be easy to find. Every time we transfer energy from one form to another, e.g. potential energy in the form of electricity to kinetic energy in a rotating motor, car engine (potential energy in gasoline to kinetic energy in the moving car) elevator operation, gas furnace(potential energy of gas to heat in house)......Any transfer of energy will be a less than 100% transfer of useful energy. The efficiency is how close you get to 100% You can thank the second law of thermodynamics for this.