If you want to edit data directly in the gridview in a 'dropdownlist' style, then you could use the 'type' => 'select' option of TbEditableColumn (YiiBooster) or EditableColumn (x-editable for Yii). This wiki shows how to get data from the db for the 'dropdownlist', by converting AR model data into an array that is passed in json format.
CFormatter is one of Yii's core components and used to format values displayed in widgets like CGridView or CDetailView. All classic formats like numbers, text, urls or datetime are supported but you may have to use a formatting rule that isn't built in. Let's say we want to display arrays of strings (like tags associated with a product model). When using CDetailView we would usually make use of PHPs implode function to create a simple string value of all values in the $product->tags array.