JRuby is an implementation of Ruby that runs on the Java Virtual Machine (JVM) and allows Ruby code to use Java classes. It supports embedding Ruby code into Java applications and using Ruby testing tools like RSpec and Cucumber to test Java code. Ruby on Rails is a highly productive web framework that is commonly used to build Software as a Service applications. JRuby allows running Rails applications on the JVM and deploying them in Java application servers. The document discusses strategies for using JRuby and Rails in both new "greenfield" projects and existing "brownfield" Java applications.