Kubernetes Service Deployment
A service proxy runs on each node on the cluster. From inside the cluster, when you make a request to a service IP, it is intercepted by the service proxy and routed to a pod matching the label selector for the service. If you have specified an external load balancer for your service, the load balancer will pick a node to send the request to, at which point it will be captured by the proxy and directed to an appropriate pod. If you are using public IPs, then your router will send the request to the node with the public IP where it will be captured by the proxy and directed to an appropriate pod.
If you followed by description, you can see that service requests do not go through the master. They bounce through a proxy running on the nodes.
As an aside, there is also a proxy running on the master, which you can use to reach nodes, services, pods, but this proxy isn't in the packet path for services that you create within the cluster.