Killers can only see the Stain at the beginning of the match; they cannot see it during the game. Survivors are able to see the Stain on the floor in front of the direction the Killer is facing. Survivors that are being chased may see the Stain slowly edge closer over time, due to the fact that killers are able to walk faster than survivors.
The Stain can potentially betray the Killer's position and movement, as survivors can see it edging out from around corners even if they cannot actually see the Killer. A clever Killer can walk backwards or sideways around corners, or walls to prevent survivors from being able to see the stain this way.