Torquebox is a Ruby application server built on JRuby, designed for rapid application development within enterprise Java environments, offering features like messaging, jobs, caching, services, and clustering. Its installation involves setting up Ruby, JRuby, and relevant gems, followed by creating a Rails application and deploying it on Torquebox. Key functionalities include background jobs, scheduled tasks, and caching solutions, along with considerations for threading and compatibility with certain Ruby libraries.