What is a Theme textdomain?

In this case, 'themify' is the defined textdomain for the Theme, used to make the Theme translatable. (Codex reference: load_theme_textdomain()).

Making a Theme translation-ready requires a few steps.

1. Define the Theme’s textdomain:

   load_theme_textdomain( 'themify', TEMPLATEPATH.'/languages' );
   

2. Define translatable strings in the template.

   This is done using one of a few translation functions: __() (for returned strings), _e() (for echoed strings), and _x()/_ex() (for gettext context strings). There are others, but you get the idea…

   A static text string, such as <p>Hello world!</p>, is wrapped in an appropriate translation function, such as <p><?php _e( 'Hello World!', 'themify' ); ?></p>, to make it available for translation.

3. Generate the .mo/.po files
   _{reference on how to edit language files}