Segundo está documentação da Amazon. Este é um recurso de balanceamento que permite direcionar os usuários para uma instância específica do balanceador.
"By default, a Classic Load Balancer routes each request independently to the registered instance with the smallest load. However, you can use the sticky session feature (also known as session affinity), which enables the load balancer to bind a user's session to a specific instance. This ensures that all requests from the user during the session are sent to the same instance."
fonte:https://docs.aws.amazon.com/elasticloadbalancing/latest/classic/elb-sticky-sessions.html