The letter was addressed to the bishops of Gaul. It is an answer to the pleas of Bishops Prosper and Hilarius, who were asked by Presbyters Theodore and Camillus about the Augustinian doctrine of grace and predestination. Prosper answered them separately ("Pro Augustino responsiones ad excerpta Genuensium").
Celestine's letter defends the doctrine of Augustine and rebukes the Gaulish bishops for allowing presbyters too much freedom in preaching.
It is interesting to see the parallel made by the pope between the presbyters and the "doctors" from 1 Cor 12, the third of the groups of the Church ministers mentioned by St Paul in the passage (after the apostles and prophets).