This means to put in effort, either with your body or mind, to do or achieve something. It can be physical or mental work.
She exerted all her strength to open it.
He exerted his mind to solve the problem.
This use means to apply a physical force or pressure on an object to make it move or change.
She exerted pressure on the handle to open the door.
He exerted force to move the heavy box.
This meaning means to work very hard or put extra energy into a task or activity, often to achieve something difficult.
He exerted himself to finish the race.
She exerted extra effort in school work.
This use is about using power or pressure to affect a person or group’s choices or decisions.
They exerted pressure on the government to change laws.
Parents exerted influence on the school's decision.