J. I. Packer defines penal substitutionary atonement:
“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.”
--“What Did the Cross Achieve? The Logic of Penal Substitution,” Tyndale Bulletin 25 (1974): 25.
Charles Spurgeon says the following, not defining it but illumining its importance, which I find helpful in light of current discussions (Gundry, Chalke, EC).
"Brethren, there will be no uncertain sound from us as to the atonement of our Lord Jesus Christ. We cannot leave the blood out of our ministry, or the life of it will be gone; for we may say of the gospel, 'The blood is the life thereof.' The proper substitution of Christ, the vicarious sacrifice of Christ, on the behalf of His people, that they might live through Him—this we must publish till we die."
In another place he presses his point home just as strongly: “Beloved brethren, we must be most of all clear upon the great soul-saving doctrine of the atonement; we must preach a real bona fide substitutionary sacrifice, and proclaim pardon as its result.” Spurgeon then explains why he is so adamant about this:
"Cloudy views as to atoning blood are mischievous to the last degree; souls are held in unnecessary bondage, and saints are robbed of the calm confidence of faith, because they are not definitely told that 'God hath made Him to be sin for us, who knew no sin, that we might be made the righteousness of God in Him.' We must preach substitution straightforwardly and unmistakably, for if any doctrine be plainly taught in Scripture it is this."
--Lectures to My Students (Grand Rapids: Zondervan, 1954), 222, 339.