The Department of Domestic Security and Defense was the designation of William Stryker's official government department assigned to deal with the mutant problem.
Following the events taking place at Liberty Island, Magneto was captured by the US Government, and was handed over to William Stryker's department, owing to his experience with mutant affairs. The Department constructed a plastic prison to contain Magneto, thereby nullifying his powers and rendering him unable to escape.
Having Magneto locked up in his custody, Stryker took it upon himself to coerce crucial information from him through his son's spinal fluid, and discovered the existence of Xavier's telepathic enhancer Cerebro. He stored the data for Cerebro on his computer at the Department of Domestic Security and Defense, to be constructed at Stryker's base in Alkali Lake.
Next, William Stryker brainwashed Nightcrawler and ordered him to assassinate President McKenna, in order to vilify mutants and justify an attack on Xavier's X-Mansion to access Cerebro for his Department database. This having failed, Stryker pleaded with the President to ordain an attack on Charles Xavier's mansion in Westchester, using this as a pretext to enable his department to gain access to Xavier's Cerebro in an attempt to replicate its abilities.
After Stryker is killed at Alkali Lake, Charles Xavier and the X-Men meet with President McKenna to disclose details regarding Stryker's true agenda, and the Department of Domestic Security and Defense is shut down, and later revamped into the Department of Mutant Affairs with Hank McCoy serving as Secretary.