The executive branch shall construe the provisions of H.R. 3199 that call for furnishing information to entities outside the executive branch, such as sections 106A and 119, in a manner consistent with the President's constitutional authority to supervise the unitary executive branch and to withhold information the disclosure of which could impair foreign relations, national security, the deliberative processes of the Executive, or the performance of the Executive's constitutional duties.But if the President has "constitutional authority to supervise the unitary executive branch," then "performance of the Executive's constitutional duties" simply means "to carry out the President's orders." So the signing statement effectively says: "The Executive will withhold information from Congress if the President wants."
The executive branch shall construe Title X in Division A of the Act, relating to detainees, in a manner consistent with the constitutional authority of the President to supervise the unitary executive branch and as Commander in Chief and consistent with the constitutional limitations on the judicial power, which will assist in achieving the shared objective of the Congress and the President, evidenced in Title X, of protecting the American people from further terrorist attacks.I don't see anyone to whom the Executive is accountable for proving that torture is necessary to prevent terrorism. That's simply a judgement the Executive makes of itself. So the translation is: "The Executive will be free to torture detainees if it wants."
You can see all of the signing statements are available online in the Weekly Compilation of Presidential Documents. Try searching for "signing AND statement". If you read a few of them, it'll be clear that the President is using these statements as a "line-item veto" — instead of vetoing an entire bill, he's just crossing out whatever parts of bills he doesn't like. In 1998 the Supreme Court decided that the line-item veto is unconstitutional. What Bush is doing is even worse: a line-item veto goes back to Congress for approval, but a signing statement does not.
That phrase "unitary executive" keeps showing up in these statements. As usual, Wikipedia has a good article explaining what "unitary executive" means. It amounts to a claim that the President has complete power over the Executive. And a lot of these signing statements amount to saying, "Since the Constitution gives me complete power over the Executive, I can ignore any laws passed by Congress." I cannot see how the unitary executive theory could possibly be compatible with the constitutional separation of powers.