Swinburne distinguishes between the logical problem of evil (the claim that God's existence and evil's existence are logically incompatible) and the evidential problem (the claim that the amount and distribution of evil makes God's existence improbable). He accepts that the logical problem has been largely solved by the free will defence: God could have created beings without free will, but beings with free will who sometimes choose evil are better than beings without free will who always do the right thing. The evidential problem is more serious and requires a positive theodicy.
Swinburne's theodicy begins with the claim that moral agency — the genuine capacity to choose between good and evil and to be responsible for that choice — is among the highest goods. A world in which people face real moral choices, bear responsibility for them, and can develop morally through their choices is better than a world of moral automata or a world in which God constantly intervenes to prevent bad choices from having bad consequences. Natural evil (disease, natural disaster) provides the framework for moral development: courage, compassion, and perseverance only have meaning against a backdrop of real suffering that can be alleviated or endured.
Swinburne acknowledges the limits of his theodicy: he cannot explain why the amount of suffering in the world is proportionate to the good it produces, or why innocent children suffer for the moral education of adults. His response is that we are in no position to know what a universe optimal for soul-making would look like, and that our intuitions about what is excessive suffering are unreliable guides to what an omniscient being would judge proportionate. Critics including William Rowe and Eleonore Stump have found this response insufficient; Swinburne's defenders regard it as a rational response to the limits of human perspective.
Swinburne's theodicy is developed in Chapter 11 of The Existence of God and in more detail in Providence and the Problem of Evil (1998). The Irenaean tradition he draws on was developed by John Hick in Evil and the God of Love (1966).