From Wikipeida:
Martial law is the imposition of military rule by military authorities over designated regions on an emergency basis—(usually) only temporary—when the civilian government or civilian authorities fail to function effectively (e.g., maintain order and security, and provide essential services), when there are extensive riots and protests, or when the disobedience of the law becomes widespread.
Here are a few points that need to keep in mind:
1) Only a fraction of the National Defense Authorization Act for Fiscal Year 2012 bill contains this, so the whole bill doesn't revolve around martial law.
2) Obama's not exactly thrilled about signing that bill for that exact part.
3) Expect that part of the law to be challenged and taken to the Supreme Court, as there are several arguments that this is a violation of the 4th amendment:
The right of the people to be secure in their persons, houses, papers, and effects, against unreasonable searches and seizures, shall not be violated, and no Warrants shall issue, but upon probable cause, supported by Oath or affirmation, and particularly describing the place to be searched, and the persons or things to be seized.
For those curious, this is the section Bryan is referring to, and the various other parts of the bill regarding increased power within the Executive Branch and the affect on U.S. citizens. I will speak no further on this matter.
(c) DISPOSITION UNDER LAW OF WAR.—The disposition of a
person under the law of war as described in subsection (a) may
include the following:
(1) Detention under the law of war without trial until
the end of the hostilities authorized by the Authorization for
Use of Military Force.
(2) Trial under chapter 47A of title 10, United States
Code (as amended by the Military Commissions Act of 2009
(title XVIII of Public Law 111–84)).
(3) Transfer for trial by an alternative court or competent
tribunal having lawful jurisdiction.
(4) Transfer to the custody or control of the person’s country
of origin, any other foreign country, or any other foreign entity.
(d) CONSTRUCTION.—Nothing in this section is intended to limit
or expand the authority of the President or the scope of the
Authorization for Use of Military Force.
(e) AUTHORITIES.—Nothing in this section shall be construed
to affect existing law or authorities relating to the detention of
United States citizens, lawful resident aliens of the United States,
or any other persons who are captured or arrested in the United
States.