Icinga Web 2 requires some components to fully run. In order to avoid building your own LAMP stack with PHP, Apache/Nginx, MariaDB, OpenLDAP, etc. just use the development Vagrant box.
PHP IDE
Icinga developers prefer to use JetBrains PHPStorm for development - basically you can use any editor you like. Just make sure to respect the indent used in the source code.
Tipp: You can apply for an Open Source license for JetBrains.
Docker Images for Development
In this blogpost on the matter you can read all about how to use docker for the developent of Icinga Web 2 and its modules.
The official Icinga 2 Docker GitHub repository and Icinga DB Docker GitHub repository can provide some more help.
The Vagrant Environment is deprecated
The documentation used to provide a quickstart on the matter. What was previously happened in Vagrant will be moved to Docker environments as described above.