Commodore is a
rank in the
Royal Navy, equivalent to
Air Commodore in the
RAF (because RAF officer ranks are mostly based on the navy's) and
Brigadier in the
Army and
Royal Marines.
In all the services it is a somewhat estranged rank; it exists immediately before the 'top brass' ranks (General in the army, Admiral in the navy and Marshal in the RAF) but above most of the more common ranks. Indeed, it often appears as one of these, in systems based on the British: Commodore-Admiral and Brigadier-General have both existed at some point somewhere. This is reflected in the insignia: Ranks below commodore are indicated by increasing numbers of stripes, whereas commodore is a single thicker stripe. Beyond commodore normal stripes are added on.
Whereas admirals get proper flags, commodores have a burgee.