RDS stands for Relational Database Service. You can select from database engines such as PotgreSQL, MySQL, Oracle, and amazon's Aurora.
Pricing can get expensive but the AWS free tier, per month, gives you 750 hours of Single-AZ db.t2.micro instance running mySQL, MariaDB, PostgreSQL, Oracle, or SQL Server. You also get 20GB of general storage, and 20GB of backup storage.