Disclaimer: I am somewhat making those terms up myself; they're not an industry standard term as far as I know. :-)

By horizontal extensibility, I mean things like form_alter. Modules can extend Drupal "sideways".

By vertical extensibility, I mean replacing existing systems or behavior rather than augmenting them.

For example, there are hooks for modules to add new stuff to the search system. There is no built-in support for changing the search engine itself, however, without disabling the search module and starting entirely from scratch.

Have a look at the first diagram in the remote data blog I posted recently. That should make it clearer what I mean. You can add more stuff horizontally next to what's already there, but changing what's already there in the stack is harder than it should be. That is, however, something that OO is inherently very good at. You just have an object that conforms to an interface, and then you can swap it out for another object of the same interface and keep working (assuming the way you instantiate the object is properly designed).

See the blog posts mentioned in the Handlers issue (the first "here" link in the summary) for extensive background on the subject.