The meaning is pretty clear: you don't manage compute, it scales up elastically based on demand, even all the way to zero. Ideally, it reacts quickly enough to changes in demand that you don't need to worry about it. Serverless is basically the original promise of the cloud.
It's not as clear as you think, because companies are watering it down. Just have a look what "serverless"-branded services AWS published the past years.
Take "OpenSearch Serverless" for example: They claim "you only pay for the resources consumed by the workload", but even if you have an OpenSearch Serverless collection you don't use, you pay at least ~$690/month (and that's not even accounting for stored data)!
