J.I. Packer:

The notion which the phrase ‘penal substitution’ expresses is that Jesus Christ our Lord, moved by a love that was determined to do everything necessary to save us, endured and exhausted the destructive divine judgment for which we were otherwise inescapably destined, and so won us forgiveness, adoption and glory. To affirm penal substitution is to say that believers are in debt to Christ specifically for this, and that this is the mainspring of all their joy, peace and praise both now and for eternity.

[ . . .] Surely the primary issue with which penal substitution is concerned is neither the morality nor the rationality of God’s ways, but the remission of my sins; and the primary function of the concept is to correlate my knowledge of being guilty before God with my knowledge that, on the one hand, no question of my ever being judged for my sins can now arise, and, on the other hand, that the risen Christ whom I am called to accept as Lord is none other than Jesus, who secured my immunity from judgment by bearing on the cross the penalty which was my due. The effect of this correlation is not in any sense to ‘solve’ or dissipate the, mystery of the work of God (it is not that sort of mystery!); the effect is simply to define that work with precision, and thus to evoke faith, hope, praise and responsive love to Jesus Christ.

[ . . . ] Faith is a matter first and foremost of looking outside and away from oneself to Christ and his cross as the sole ground of present forgiveness and future hope. Faith sees that God’s demands remain what they were, and that God’s law of retribution, which our conscience declares to be right, has not ceased to operate in his world, nor ever will; but that in our case the law has operated already, so that all our sins, past present and even future, have been covered by Calvary. So our conscience is pacified by the knowledge that our sins have already been judged and punished, however strange the statement may sound, in the person and death of another.

» Gospel Gold from J.I. Packer’s excellent article, “What Did the Cross Achieve? The Logic of Penal Substitution