A serverless database refers to a cloud-based service where users can store and manage data without worrying about managing servers, scaling resources, or handling administrative tasks. This approach is designed to eliminate the operational burden of traditional databases, allowing developers to focus on their applications' functionality. Serverless databases are highly scalable and resource-efficient, as they automatically adjust to changing workloads and only charge for the actual usage. Neon, a serverless Postgres platform, aims to make databases just a URL, simplifying management and reducing costs for both individual developers and large organizations.