When you fail a Reflex Save against an effect for half damage, you only take half damage.
Automatic Grant:
This feat is granted free to Monk at class level 9
This feat is granted free to Dragon Disciple at class level 9
Bonus Classes:
Rogue
Notes:
Only works if you're wearing light armor, not wielding a heavy or tower shield, and not heavily encumbered. Does not work when you're helpless.
Can't be taken without having the Evasion feat, which says that when you succeed on a Reflex Save for half damage, you take no damage instead of half damage.