The value of J = 2 corresponds to the situation where L and S are pointing in the same direction (and parallel). The J = 0 state is where L and S are pointing in opposite direction (ans parallel). Lastly, the J = 1 state corresponds to L and S being perpendicular. This can be easily understood from the equation J = L + S. Or thus J² = L² + S² + 2 L*S.
Thus if L and S are in the same direction, a positive contribution arises, if they are perpendicular just the first 2 terms remain, and when opposite it gives a negative contribution.