This is something I've gladly inherited from The Sandbox. Here's the documentation from the Sandbox readme:
Comments are not displayed on pages by default, but are displayed on posts, per the current convention. You can enable comments on a per page basis by adding a custom key/value with only the text comments.
To enable comments on a page:
1. In the Write › Page menu, expand the Custom Fields box
2. In the Custom Fields box, add a new key with the exact text comments
3. Add any text for a value (some text must be included for the key to save)
4. Click Add Custom Field to save the key/value
5. Comments should now be enabled on that page
Enabling comments simply includes the comments.php file with the page. You can turn off comments on a page by deleting the comments key/value. This does not delete any exisiting comments, but simply disables comments.php from loading with the page.