It explains exec. orders a little more:
Executive Orders
In times of emergency, the president can override congress and issue executive orders with almost limitless power. Abraham Lincoln used an executive order in order to fight the Civil War, Woodrow Wilson issued one in order to arm the United States just before it entered World War I, and Franklin Roosevelt approved Japanese internment camps during World War II with an executive order. Many other executive orders are on file and could be enacted at any time.
I think the key portion there is: "In times of emergency."
Wikipedia is also helpful in clarifying what can and cannot be done with exec. orders:
Until the 1950s, there were no rules or guidelines outlining what the president could or could not do through an executive order. However, the Supreme Court ruled in Youngstown Sheet & Tube Co. v. Sawyer, 343 US 579 (1952) that Executive Order 10340 from President Harry S. Truman placing all steel mills in the country under federal control was invalid because it attempted to make law, rather than clarify or act to further a law put forth by the Congress or the Constitution. Presidents since this decision have generally been careful to cite which specific laws they are acting under when issuing new executive orders.
Wars have been fought upon executive order, including the 1999 Kosovo War during Bill Clinton's second term in office. However, all such wars have had authorizing resolutions from Congress. The extent to which the president may exercise military power independently of Congress and the scope of the War Powers Resolution remain unresolved constitutional issues, although all presidents since its passage have complied with the terms of the Resolution while maintaining that they are not constitutionally required to do so.
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