Inspiration Boost is a star within the Constellation The Tower in Elder Scrolls Online (ESO).
This was added in Update 6 with the Champion System. It grants the player a permanent 20% Inspiration gain. 30 points in the Tower Constellation are required to unlock it, at which point the bonus will be applied automatically to all of that character's inspiration gain.
As with all other CP unlocks, these points must be allocated in the champion point interface of each character for which you wish to have this unlocked: the unlock is per-character, rather than account-wide.