A static force refers to a constant force applied to a stationary object. A static force is too weak to move an object because it is being countered by equally strong opposite forces.
The most common example of a static force is static friction on a stationary object. If an object has some force being applied to it while it is on a surface, the force of friction will increase proportionally to the force until a certain limit. If the applied force is large enough, it can overcome the static friction and move the object. The force is then a kinetic force that is being resisted by kinetic friction.