This option gives you the ability to enable/disable the horizontal resizing. This option is only useful if the theme_advanced_statusbar_location option is set to "top" or "bottom" and when the theme_advanced_resizing is set to true. This option is set to true by default, that makes resizing horizontal and vertical.
Example of usage of the theme_advanced_resize_horizontal option:
tinyMCE.init({
...
theme_advanced_resize_horizontal : false
});