The Drafš Kāvīāni or Drafš-e Kāvīān (the Standard of Kāveh) was the legendary royal banner of ancient #Persia and a symbol of #Iranian nationalism and monarchism. It has never been recovered, being burned by the Rāshidūn after their conquest of the Sassanid Empire.
Kāveh is a figure in Iranian mythology and features an important role in the #Shahnameh. According to legend, he was a blacksmith (cfr. the Ergenekon) that lead the Iranian people against the tyrant Zahāk by brandishing a flag he made from attaching his leather apron to a spear.
Kāveh the Blacksmith is still a revered figure within Iranian nationalist movements, and a pro-German periodical of the same name was published twice a month between 1916 and 1922. Its title page showed Kāveh leading Iranians while brandishing his Drafš Kāvīāni.
The oldest recorded instance of this vexillological symbol is the so-called #Pazyryk carpet, manufactured in ancient Persia around 400 BC. The wool carpet was part of a #Scythian nobleman's tomb high in the Altai Mountains. It was probably gained through trade with #Persia.
Although the exact origin of the Drafš Kāvīāni symbol remains unknown, it's certain that it started to feature a royal role since at least #Seleucid times. A 3rd c. BC coin of Vādfradād I, governor (Frataraka) of Persis, shows him with the Drafš Kāvīāni in remarkable detail.
A more "recent coin", from Bagadates I, the 2nd c. BC governor (Frataraka) of #Persis, also shows him seated on his throne while in the presence of the Drafš Kāvīāni, again exquisitely detailed. From these coins we can imagine how the standard looked like in real life.
Only under #Sassanid rule (224–651 AD) grew the famed Drafš Kāvīāni into a tangible imperial banner surpassing local flags and standards. According to the Encyclopedia Iranica, the banner had a bejeweled purple background, a star as the central emblem and four streamers.
Based on the coins and the description of the Encyclopedia Iranica, the imperial #Sassanid banner may have looked something like this, in addition to the purple background being heavily bejeweled. The central element is a star (akhtar) and it has red, purple and gold streamers.
Popular modern depictions, however, represent the central star (akhtar) as a flower-like figure and a dot in each quadrant of the flag, sometimes totaling four but mostly limited to one in the upper quadrant. These flags are a direct reference to #Sassanid imperial reign.
There are, however, other ways to represent the Drafš Kāvīāni without its Sassanid set-up. The presidential standard of Tajikistan (to your right), for example, features the famous Drafš Kāvīāni symbol in a completely different set-up while keeping distinct Iranian symbols.
The star is replaced by a winged lion. The dots have been removed, now appearing as a star in each corner of the emblem. The upper quadrant now features the crown emblem of #Tajikistan. The four streamers are kept and the whole is set to a background of red, white and green.