Computed Property Theory & Best Practices or Functional Programming in Ember or How I learned to stop worrying and love the Tomster.
In a nutshell, computed properties let you declare functions as properties. You create one by defining a computed property as a function, which Ember will automatically call when you ask for the property. You can then use it the same way you would any normal, static property. -- The Ember Guides
The Ember Object Model is the corner stone of Ember, and at the heart of the Object Model are computed properties.
The guides do a fine job giving need to know information on how to create and use computed properties and what to expect from the cacheing system they provide. However, I feel so much of the beauty that computed properties provide is lost in terse (but wonderful) documentation.