You can run Mendix in your development environment using the so-called 'built-in database'. This is a database implementation that entirely runs inside the working memory that is allocated to the mendix process itself. This is convenient for adding a little amount of test data without having to configure an additional database system like PostgreSQL or MS SQL Server.
But! If you want to work with more data than just that 'little amount of test data that easily fits into memory', yes, you need to run a database server itself, which you connect the Mendix server process to. In this case, your database can be as large as the external database system can handle.