Aurora Serverless is an on-demand, auto-scaling configuration for Aurora (MySQL-compatible edition) where the database will automatically start-up, shut down, and scale up or down capacity based on your application’s needs. Aurora Serverless enables you to run your database in the cloud without managing any database instances. It’s a simple, cost-effective option for infrequent, intermittent, or unpredictable workloads, because it automatically starts up, scales capacity to match your application’s usage, and shuts down when not in use.

Manually managing database capacity can take up valuable time and can lead to inefficient use of database resources. With Aurora Serverless, you simply create a database endpoint, optionally specify the desired database capacity range, and connect your applications. You pay on a per-second basis for the database capacity you use when the database is active, and migrate between standard and serverless configurations with a few clicks in the Amazon RDS Management Console.

Source: Amazon Aurora Auto-Scaling Serverless Database Service - AWS

$0.06 per “Aurora Compute Unit” per hour, but you pay prorated by the second… This is a very interesting option for inexpensive database servers.