Preter refers to something prior, as in the Latin sense of the preposition praeter, meaning “prior” or “beyond”.
The three “preternatural gifts” (the three I’s: infused knowledge, immortality, and integrity) are preternatural in the sense they do not belong to bare human nature, while at the same time they are not supernatural. In other words, the preternatural gifts strengthen human nature, but are not habits of grace. They bring out the best of what human nature could be.
This is an important feature of Catholic anthropology. A) It resists the Calvinist doctrine of “total depravity” because Original Sin causes man to fall to bare human nature. The Fall is the removal of a set of gifts, strictly speaking. B) It also allows us to understand how redemption is accomplished through Christ – that we are reconstituted in sanctifying grace through Christ. C) It may be helpful with understanding an evolutionary origin of mankind, in that human beings were not created as “naturally” immortal, but that this immortality was something “preternatural”. Immortality was a gift that was forfeited.