What exactly is a headless service, what does it do/accomplish, and what are some legitimate use cases for it?

Well, I think you need some theory. There are many explanations (including the official docs) across the whole internet, but I think Marco Luksa did it the best:

Each connection to the service is forwarded to one randomly selected backing pod. But what if the client needs to connect to all of those pods? What if the backing pods themselves need to each connect to all the other backing pods. Connecting through the service clearly isn’t the way to do this. What is?

For a client to connect to all pods, it needs to figure out the the IP of each individual pod. One option is to have the client call the Kubernetes API server and get the list of pods and their IP addresses through an API call, but because you should always strive to keep your apps Kubernetes-agnostic, using the API server isn’t ideal

Luckily, Kubernetes allows clients to discover pod IPs through DNS lookups. Usually, when you perform a DNS lookup for a service, the DNS server returns a single IP — the service’s cluster IP. But if you tell Kubernetes you don’t need a cluster IP for your service (you do this by setting the clusterIP field to None in the service specification ), the DNS server will return the pod IPs instead of the single service IP. Instead of returning a single DNS A record, the DNS server will return multiple A records for the service, each pointing to the IP of an individual pod backing the service at that moment. Clients can therefore do a simple DNS A record lookup and get the IPs of all the pods that are part of the service. The client can then use that information to connect to one, many, or all of them.

Setting the clusterIP field in a service spec to None makes the service headless, as Kubernetes won’t assign it a cluster IP through which clients could connect to the pods backing it.

"Kubernetes in Action" by Marco Luksa

Simply put, a Headless service is the same as default ClusterIP service, but lacks load balancing or proxying. Allowing you to connect to a Pod directly.

I think the most common use case is mainly attributable to StatefulSets, that currently required a Headless Service. See why-statefulsets-cant-a-stateless-pod-use-persistent-volumes when you might use one...