After, selecting the installation profile, the installation script will check if all the system requirements needed to install Drupal are complete or not. You might be shown warnings or errors accordingly. These should be resolved in case you are setting up a production website as these can later introduce issues on your website. For learning purposes, you can ignore all these warnings.
After verifying system requirements, the installation script will ask for database credentials. It will also try to establish a connection with the database and give an error in case there are any issues.
Since I am using Acquia Dev Desktop, I didn't see any errors related to system credentials and connection with MySQL (which is bundled with Acquia Dev Desktop) is also automatically handled as well.
The actual installation begins after these steps. Based on the packaged modules and configuration in the installation profile, Drupal starts a batch process of installing them. Don't worry in case you do not have a full understanding of all these terms and what's actually happening in the back end at this moment.