Bow Expert is a star within the Constellation The Atronach in Elder Scrolls Online.
This was added in Update 6 with the Champion System. It increases the damage of your Light and Heavy Attacks with Bows by [x]%. You can put 100 Champion Points into this passive ability for a maximum of 25%.
With each point invested, the increase in the Light and Heavy Attack Damage dealt with Bows diminishes. That is to say, for the first 10 CP invested, you would gain a 5.0% increase in Damage. However, the next 10 CP spent (making a total of 20 CP spent), will earn you only 3.1% more Damage. This is 1.9% less than the increase gained in the first 10 CP.
As such, spending just 37 CP into Bow Expert will already gain you a 12.5% increase in Light and Heavy Attack Damage dealt with Bows. This means you will have gained 50% of the Maximum increase possible (which is 25.0%) by spending just 37 out of the total of 100 CP. Therefore, beyond this point, the increase in Damage received per 1 CP used is very small and not as worthwhile.