CockroachDB Serverless offers a truly serverless database experience by allowing automatic scaling of resources based on workload, ensuring that users only pay for what they use, and potentially allowing them to use the service for free indefinitely. Unlike some serverless databases that do not scale down to zero, CockroachDB Serverless guarantees scaling to zero, meaning no charges occur when there is no activity. It provides a free initial tier with monthly credits for requests and storage, and users can set spend limits to avoid unexpected charges while receiving alerts as they approach these limits. The service is designed to handle surges with "burst capacity" and offers tools for managing and optimizing serverless workloads, making it an attractive option for developers seeking cost-effective and efficient database solutions.