Dragons were originally depicted worldwide as serpents, but during the middle ages dragons began being depicted with legs similar to a lizards. Western dragons are traditionally described as living in rivers or caves, having a thick armour-like hide, and never flying despite often being depicted with wings. Western dragons are usually evil creatures who are greedy and hoard gold and other treasures in their caves. This is due to them being demonized due to the rise of Christianity in Europe. Many dragons before this were seen as benevolent creatures such as Y Ddraig Goch or the Red Dragon of Wales. The two headed dragon is often seen as a symbol of the division between the Eastern and Western Roman Empires.
Russian dragons are similar to hydras in the fact that they have three heads and if each one isn’t cut off at the same time they will grow back. Other Russian dragons most likely symbolize the Mongols and other peoples of the steppes.
In Asian dragons especially those found in Indian mythology often have their roots in religion. In the early Vedic religion, Vritra or “the enveloper” was the personification of drought. Chinese dragons are amalgamations of all the other Chinese Zodiac animals. For instance a Chinese dragon has the body of a snake and the front legs of a rooster. In Japan most dragons are water deities associated with rainfall and bodies of water. In Vietnam dragons bring rain.
Dragons in modern media are either described as being benevolent and wise, greedy and cruel, or creatures of mass destruction. Another description has been gaining prevalence as of late. Dragons are now being described as being lonely and misunderstood more and more.
This post barely goes into depth with any of the dragons I have described, and I even ended up skipping a couple. There are many dragons described in myths around the world and each one is different in its symbolism than the last. Keep this in mind when writing dragons as symbols in your stories.