Habeas corpus is important to the current situation because it has to do with the right of defendants to be charged with a crime and tried for that crime in a timely manner.
Under the right of habeas corpus, the government must justify their detention of any person. They must show why they have the right to hold that person. If they cannot, they must release them. In the current war on terror, there is controversy as to who has the right to habeas corpus. There is controversy as to whether the government can simply hold people for long periods of time as "enemy combatants" without charging them with a specific crime.