Components put you in control of the destiny of your Rails application. Decompose your existing application to make it more maintainable and to set you up for a bright development future. Assemble your new application from smaller pieces that you can develop concurrently, combine reliably, and test independently.
Good examples on starting using component based approach. Book answers for at least three questions about components in Rails: What they are? Why components? And how they can be implemented and used? Easy and in a fun way it described in a terms of power, simplicity and beauty of Ruby language. A lot of useful examples and techniques can be applied not only for component based apps. They are generally useful for many approaches.
Great book, both with hands-on code examples and higher level strategy and tactic tips. This is a great reference about Rails engines. It will help you refactoring legacy applications and building new ones from scratch (it's really helping me, at least). If there were a "Rails: the good parts" book it should certainly cover #CBRA approach.
Some sections (hexagonal architecture, for example) have room for improvement, but anyway I'd really recommend this approach for real-world Rails applications, beyond the artificial, fake examples that other references are based on.