Each task can be tagged with one or more flags to make it easy to visually categorize them in Card View. This dialog is used to configure the flags for the current board and to select which flags to apply to the current task.
This bar represent the color of the flag as it shows in card view. You can click in the bar and type text to appear in the flag. Note that by changing the text that appears here you are changing it for all flags of that color in the whole board, not only for the current task.