We know that, F=ma, where F is the force, m is the mass of the object and a is the acceleration with which the object moves.
Hence, as per the equation given above the applying force should be either equal to or greater than the mass of the object.
If it is not the case, then the object will not move. So, for the object to move we need to apply a greater force, when the applied force is greater then the object moves faster and vice versa