I'm currently working with Groovy and Grails. While Groovy is pretty straight-forward since it's basically Java, I can't say I grok Grails. I read that Groovy is to Grails as Ruby is to Ruby on Rails, but what does that mean?
Ruby on Rails is a web application framework for the Ruby programming language. Grails and others are Rails-like frameworks for other languages.
Rails is a framework for developing web applications with a database back-end. I think the name originally was a play on words. A train can take you somewhere really fast, but only where the rails go.
It's an automotive expression. When a car handles exceptionally well, it's said to "corner like driving on rails" (i.e. it gives you excellent control).
I don't know if that's where the rails people got that name, but that's how I interpreted it.
It's a metaphor, and I'm almost said that needs explaining. Anyway, it's an extremely good metaphor for what Ruby on Rails does. It makes it extremely easy to do (go to) the common stuff, i. e. testing, validation, deployment, MVC.
I think a framework that strives to be "rails-like" refers to several things:
model-level: an AR-patterned ORM (rather than datamapper), migrations or some automated schema and model-layer management, handling foreign keys in the application (not in database schema, and also not using stored procedures or pure DBMS logic)
TDD encouraged: automatically generated skeletons for unit-tests,
naming conventions connecting database table names and model names, controller and view actions and HTML templates
streamlined route recognition and route generation scheme
emphasis on REST architecture
integration with ajax libs: RJS, prototype and scriptaculous
To address your confusion with the metaphor (though it has been answered in other words under your question):
Groovy is to Grails as Ruby is to Ruby on Rails, but what does that mean?
Grails was a web framework built on/with the Groovy programming language to do the same thing for Groovy that Rails (a web framework for Ruby) does for Ruby.
What does it mean to be "on rails"?
The answer to this comes down to the essence of these web frameworks.
These web frameworks (Grails & Rails) are built on the premise of "convention over configuration", which means that using common conventions to develop web applications can lead to higher productivity and more maintainable applications (this is a gross generalization). And by defining a convention and sticking to that you will find that your applications are easy to generate and quick to get up and running.
This is what it means to me to be "on rails", just like a train. When a new train route is developed there is no worry about reinventing the way the train will get from one place to another, it's been solved by a single convention for decades: rails. Just as the tracks on a train route constrain its path from two locations, convention-based web frameworks use conventions to the flexibility of application developers so that they can concentrate on what the essential business problem of their application.
One key benefit of a convention for a web framework is that the web framework can now make assumptions on how certain layers of the application hook together. In Rails, one can usually assume that if one's database table has a plural name, the ActiveRecord class mapped to that table will have the corresponding singular name. Consequently, Rails code generators can consume the data-mapping information to generate data access code such as dynamic finders, migrations, lazy-loaded association traversals, etc. This data access code in a configuration-based framework is laborious to code by hand.
Really short and simple answer: Convention over Configuration.
As said above, Rails and Grails provide conventions for web application development -- naming your pieces a certain way and putting them in the right places get your application working by default with no extra configuration. When you want to deviate from the convention, you can configure your way there.
Several people have mentioned the technicalities of what makes Rails/Grails what they are. Several people have also mentioned "convention over configuration" as being the "rails" in Rails/Grails. This is getting closer to the truth. But this is just one characteristic of the broader philisophy of Rails, which is the concept of opinionated software.
Opinionated software can't be described in only technical terms; it's a philosophy; an ethos; an attitude. Like it or hate it, that is what's at the heart of Rails.
Here's an exceprt from a 2005 interview with David Heinemeier Hansson, creator of Rails:
Rails is opinionated software. It eschews placing the old ideals of software in a primary position. One of those ideals is flexibility—the notion that we should try to accommodate as many approaches as possible, that we shouldn't pass judgement on one form of development over another. Well, Rails does, and I believe that's why it works.
With Rails, you trade flexibility at the infrastructure level to gain flexibility at the application level. If you are happy to work along the golden path that I've embedded in Rails, you gain an immense reward in terms of productivity that allows you to do more, sooner, and better at the application level.
There is also a later interview that further explores the subject.
So being 'on rails' is a metaphor for being 'opinionated', which is why it is named as it is. That and the fact that "Ruby on Rails" is alliteratve, which any journalist or writer will tell you, is a sure-fire way of hooking people's attention.
I disagree with the other comments of "on rails is a philosophy about convention over configuration" and so on.
While rails does adhere to those philosophies, "Ruby on Rails" is the name of a web framework. Nothing more, nothing less. It's not referring to any specific "on-railsness" about it, it's just a brand name in the same way that McDonald's is a brand name.
If someone else writes another framework and calls it "Python on Rails" then there'll be another brand name. If not, "XYZ on rails" just means people are being confused.
Being on rails means you can't control where you are going. It means, you can only go where the rails have been laid. Any attempt to go where the people who laid the rails didn't anticipate you to go will lead to frustration.
Ruby and Groovy are languages.
Ruby on Rails is a ground-breaking webapp framework. See excellent answers on opinionated software above.
As a matter of history, a working title for a Groovy webapp framework was Groovy on Rails. However the RoR community objected. The team chose Grails instead.