Widget ready means a theme has widgetized areas which allow you to dynamically manipulate these areas in an easy to use drag-and-drop fashion. Most of the time widgets are used in the sidebars of themes, which is why you may frequently see the term “widgetized sidebar” in conjunction with widget-ready. Since WordPress 2.2, widgets are a part of the “core” and bundled with all new WordPress installations.
Why would you want to use widgets?
You might want to use widgets because they make changing up the sidebar (or other widgetized areas) of your WordPress site much easier. Moving around sidebar items such as category/archive listings and blogroll links can be done with ease through a widget-ready theme. You can find a huge listing over at the official WordPress plugin repository.