The Java Runtime Environment (JRE) is used to run all programs written in the Java programming language. Java 2 is required to run both Eclipse and PHPEclipse. Chances are that you will already have this installed. If not, or if you are not sure, visit Sun's Java Download Site, which will provide you with what you need (or inform you if you already have Java 2) for any operating system.
If you are using a platform with its own software management system (such as many linux distributions), you may wish to use your package management system to install Java rather than the Sun download site.
Third party Java Runtime Environments (such as Blackdown) are also available, and may well run this software. Feedback on this is welcome. Our current experience is that Blackdown will not successfully run Eclipse (under Gentoo Linux, Nov 2004).