You have the choice between HSQLDB, Microsoft SQL Server, Oracle DB, PostgreSQL server and MySQL, you can configure them in your project settings. The HSQLDB that you use by default is in the deployment/data/database folder. See https://world.mendix.com/display/refguide5/Configuration for how to configure this.
And -for Development only- you can get to the HSQLDB within the Modeler via: Console > Advanced > Start Built-in database viewer.
A HSQLDB environment is then started in which you can check and manipulate the data your Mendix App uses. Right mouse-click on an entity in the tree-of-tables to the left and you can choose from standard SQL scripts like Select, Delete, Update, Insert. Don't forget to hit the 'Execute SQL' button, otherwise it won't start the selected query.