How does the case Hamdi v. Rumsfield show the importance of a person's rights?
This is a great question and one that is important as well. Let me give you a bit of the context and then point out why this action was significant.
Hamdi v. Rumsfeld is a U.S. Supreme Court decision that overturned the dismissal of habeas corpus ("you may have the body" in Latin) for Yaser Esam Hamdi. Hamdi was a U.S. citizen that was born in Louisiana, who was detained as a enemy combatant as he was captured fighting in Afghanistan.
The Supreme Court stated that while it does acknowledge that the government has the right to detain enemy soldiers, but when the enemy soldier is also a U.S. citizen, he or she has the right to challenge their status before an judge.
This is an important development, because habeas corpus from a historic and legal point of view has been a very important safeguard for individual freedom against the government, which has much more power. This also shows that individuals, even if they turn on the country, have rights. This is a remarkable point in a democratic society.