"Anti" features in suspension systems are a characteristic that can be used to influence the stiffness of the front or rear suspension under traction forces(under braking or accelerating). The individual terms are relatively straightforward and self-explanatory with the "anti" reducing or totally restricting the characteristic (lifting or diving). In the front suspension there may be levels of anti-dive during braking and anti-lift during accelerating (assuming traction to the front wheels is present), similarly in the rear there could be anti lift during braking and antisquat during acceleration.
It should also be noted that these characteristic can also be reversed into a "pro" characteristic (as in pro-lift at the front under braking). Anti features can only be implemented under the influence of the braking or accelerating forces at the wheels, for example a rear wheel drive vehicle cannot have an anti-lift characteristic in the front (as there is no drive to the front wheels).
With the ALK fitted to the Subaru WRX, a softer suspension will be present during braking and accelerating. This will help traction, as the wheel will be able to track the ground more precisely. Also in terms of balance the front end will have a proportionally lower roll resistance during traction or braking, aiding in reducing the power understeer effect that is present in these cars.