The Skill Install System enables you to augment your gear from the craft menu with Skills using Bereaved (leftover) God Arcs found from after missions. There are 4 rarity ranks ranging from least to most rare: Green, Purple, Blue and Yellow. You can increase the rarity of God Arcs obtained after missions using Haru's card. Since the maximum effect level is Lv10, you should be keeping God Arcs of Lv5 and above so you can effect a Lv10 effect with just one or two Arcs installed.
+1s will grind the weapon up to +30 percent bonus stats to the gear it is installed to.