Just as the American soldiers, the Iraqi Mujahedeen also like to show off with body parts of their fallen adversaries. The Mujahedeen have more of a noble cause backing their actions up as they fight for freedom from the oppression by the aggressor who invaded their country. Still, showing off a severed hand before the eyes of children sends all kinds of bad signals regardless of how justified your fight is.
The limb appears to have been severed in a blast. Given that the video came from Iraq, it’s fair to assume that whomever the band belonged to probably died in an IED attack. The video of the Mujahedeen parading a severed hand of what they claim was an American soldier is below:
It is possible that the severed hand came from an American soldier killed in this IED attack on a humvee seen in this mock-video: