What is the "port" used for for a Kubernetes Service

In a nodePort service you can have 3 types of ports defined:

TargetPort:

As you mentioned in your question, this is the corresponding port to your pod and essentially the containerPorts you have defined in your replica manifest.

Port (servicePort):

This defines the port that other local resources can refer to. Quoting from the Kubernetes docs:

this Service will be visible [locally] as .spec.clusterIP:spec.ports[*].port

Meaning, this is not accessible publicly, however you can refer to your service port through other resources (within the cluster) with this port. An example is when you are creating an ingress for this service. In your ingress you will be required to present this port in the servicePort field:

  ...
        backend:
          serviceName: test
          servicePort: 80

NodePort:

This is the port on your node which publicly exposes your service. Again quoting from the docs:

this Service will be visible [publicly] as [NodeIP]:spec.ports[*].nodePort

Port is what clients will connect to. TargetPort is what container is listening. One use case when they are not equal is when you run container under non-root user and cannot normally bind to port below 1024. In this case you can listen to 8080 but clients will still connect to 80 which might be simpler for them.