The gedwëy ignasia (meaning "shining palm" in the Ancient Language) was the mark of a Rider, shining brightly whenever the Rider used his magic. It was a silver disfused spiral oval marking that appeared on the Rider's palm after the Rider first touched his dragon; depending on the Rider, this could be either the left or the right palm. Generally, the hand bearing the gedwëy ignasia was the hand the Rider used to direct his magic.
It is also called Argetlam, meaning "Silver Hand". Airgetlam, often anglicized as Argetlam, is directly out of the Lebor Gabala Erenn (The Books of Invasions of Ireland). In Old Irish it means "Silver Hand". This is, again, from the Ancient Language.
Eragon's gedwëy ignasia was on his right hand, while Murtagh's was on his left. This is probably because left-handedness is traditionally a sign of wickedness, to the extent that left-handed men in the medieval age could not become knights, because it was believed that they were the sons of the devil.