This is the first of two phases during which each damaged ship repairs some of its damage, increasing its DP by its auto-repair (AR) rating.  These repairs happen automatically and cost no RU.  A ship's operational rating (OR) is correspondingly increased by these auto-repairs.  A ship can never be auto-repaired above its original DP value.

Note that auto-repairs are always visible to any empire which has an unloaded ship in the same sector.