The Crest of Cinders is a neutral buff available on Summoner's Rift.
The buff can be identified by a spinning red rune circle around the champion. Because of this it is often referred to as the "red buff" or just "red". The damage dealt is true damage. This makes it valuable in killing champions who have high armor and magic resistance.
As of patch 6.9, the red buff slows by 10 / 15 / 25% for melee champions and 5 / 7.5 / 12.5% for ranged champions. This makes the buff more effective when utilized by melee characters such as Xin Zhao, Udyr, or Tryndamere than it does for ranged attackers such as Tristana and Ezreal. Note however that it is easier for ranged champions to apply the slow without getting in dangerous situations and they can also use it to keep melee attackers at a distance.
The jungler will most likely take the red buff early in the game.
The extra damage lets the jungler clear minion packs easier and take on bigger monsters like the Dragon.
The slow from the buff is extremely valuable for the jungler to successfully execute a gank and is also useful for kiting monsters to reduce damage.
Increasing attack speed will increase damage dealt, as the damage is re-applied as an on-hit effect.