Spring force exerted by the spring to return the spring to its unstretched state.
The minus sign takes into account the direction of the force. The force acts against the direction of deflection. For the magnitude, the minus sign may of course be omitted.
The spring constant is a material constant and depends on the spring used. It tells how well the spring can be stretched (that is how elastic the spring is).
The deflection of the spring from its neutral position. For example, if you pull on the spring, \(y\) is the distance by which the spring was deflected.