Java is the language in which the OpenMRS Platform is written. The latest released version of the OpenMRS Platform requires at least Java version 1.6 where as the head of the master branch requires java 8. You should be able to build and run supported maintenance branches with versions 1.6 or later. If you plan to edit the source, you will need the JDK; if you plan just to run the OpenMRS Platform, you will only need the JRE.
MySQL is the database software most people use for the OpenMRS Platform database. You should know your MySQL root password, or have a database ready with username and password to install the OpenMRS Platform into.
Eclipse IDE for Java EE Developers is the recommended Java development environment. Get the latest stable release (though the OpenMRS Platform should still function on older versions that can use Maven integration, see instructions for older versions).
The latest release has all plugins you need to start OpenMRS development. There is one optional plugin we recommend to install that allows you to create tests from @should annotations.
OpenMRS Platform Behaviour Test Generator (optional)
Refer to the How-To Setup And Use Your IDE to either install an IDE or configure the one you have for OpenMRS development.
Jetty, a development-oriented J2EE server, is automatically provided with the OpenMRS Platform 1.8+, via Maven, and it integrates nicely with Eclipse's Run and Debug workflows. It is perfectly sufficient for most developer purposes.