With the Inspiration perk, your companions can gain a variety of bonuses, like greater combat damage, immunity to friendly fire, and increased carrying capacity.”— Fallout 4 loading screen hints
This perk centers around making companions work more efficiently for you. The first rank causes companions to do more damage, and no longer allows them to hurt you with their attacks. The second rank causes companions to resist more damage and no longer allows them to be hurt by you. The third and final rank lets companions carry more items.