The function of an elastic load balancer (ELB) in cloud architecture is to distribute incoming application traffic across multiple targets, such as EC2 instances or containers. This helps in maintaining application availability and improves fault tolerance by ensuring that no single instance is overwhelmed with requests. ELBs automatically adjust to fluctuations in traffic, optimizing resource utilization and enhancing performance. By providing high availability and allowing for seamless scaling, elastic load balancers play a critical role in ensuring a stable and responsive cloud application environment.