Relational Databases are the software implementation of the concepts expressed by the theory introduced by the Relational Model.
In a Relational Database, data is stored in tables.
Each table contains one or more columns, that hold data of a specific type, like strings, numbers and so on.
The set of a table and all the rules about its columns is called a schema.
Each table can define constrains upon the data that each row can contain.
Tables can reference each other, forming relationships, using foreign keys.
A Database Management System is the software that implements the database in a computer system.
Commonly, relational databases use the SQL language to let us give instructions to create a database, define its tables schema, fill tables with data, and finally query the data when needed.
Some examples of software implementing relational databases are PostgreSQL, MySQL, SQLite, Oracle and MicroSoft SQL Server.