In a penalty contact solution method the contact interaction between the bodies is handled via spring elements that model the stiffness of the contact. Hence, in a penalty approach it is possible that the faces in contact penetrate each other slightly depending on the defined contact stiffness that couples the interpenetration with the consequential reaction forces. As the interpenetration causes forces that try to prevent further intersection and penalize this behavior it is called Penalty method.
The contact stiffness of a penalty contact is defined by the stiffness coefficient of the linear penetration model.
You define the linear relation between the interpenetration and the contact pressure via the Penalty coefficient. The higher you choose the parameter the stiffer the contact gets, which is desired in most cases, as you do not want the bodies to penetrate at all. However it gets harder to reach convergence for your nonlinear calculation in most cases when you increase the penalty coefficient, so you have to find a tradeoff between those counteracting interests.