Why is substitutionary atonement so important? Two reasons — one theological and one applicational.
For the first, J. I. Packer offers a summary definition of the atonement in his article, "Sola Fide: the Reformed Doctrine of Justification":
This is the characteristic doctrine of the Reformation concerning the death of Christ. It was an act of obedient substitution on his part, an acceptance in his own person of the penalty due to us, in virtue of which the holy Judge declares guilty sinners immune from punishment and righteous in his sight. The great exchange is no legal fiction, no arbitrary pretense, no mere word-game, on God's part, but a costly achievement. The divinely established solidarity between Christ and his people was such that he was in truth "made sin" for us, and "bore in his soul the dreadful torments of a condemned and lost man," so that in our souls the joy of knowing God's forgiveness and favor might reign forever. This, to the Reformers, was the heart and height of the work of divine grace, not to be wrangled over, but to be trusted and adored.
For the latter, Milton Vincent, in his book A Gospel Primer, offers a summary application of the gospel — preach it to yourself every day:
There is simply no other way to compete with the forebodings of my heart, and the lies of the world and the Devil than to overwhelm such things with daily rehearsings of the gospel.…As long as I am inside the gospel, I experience all the protection I need from the powers of evil that rage against me. It is for this reason that the Bible tells me to "take up" and "put on" the whole armor of God…
That God would tell me to "take up" and "put on" this gospel armor alerts me to the fact that I do not automatically come into each day portected by the gospel. In fact, these commands imply that I am vulnerable to defeat and injury unless I seize upon the gospel and arm myself with it from head to toe. And what better way is there to do this than to preach the gospel to my self and to make it the obsession of my heart throughout each day?