Mental strength means many things to many people. It could be staying calm with the kids for a mother and pushing to the finish line for a runner.
Strength is the state of being strong, having mental power, force. Having strength is empowering and exhibiting self-control. Without resistance there is no need for strength so when we are using our mental strength then we are up against some resistance or obstacle. Most people avoid resistance and obstacles and therefore give up their power and control.
Being mentally tough is not the same as strength. Toughness is a burden to perform or accomplish something difficult. Think of when you have a callous on your hand. At first it is rough and toughens up. It eventually thickens and then you lose all feeling in the callous. Then the callous becomes painful. When you toughen up with people, you exercise a roughness that leads to insensitivity and then pain.
It is common to confuse toughness with strength. Sometimes these terms are even intermingled and misused but keep in mind that when toughness is exercised, pain follows and when strength is exercised, power follows. Mental strength is the ability to overcome mental resistance and consciously cause goals to be achieved.