If you're a sheep farmer, sheep dipping means you're literally dipping sheep in a bath made to kill insects and fungus. It's a good way to keep your flock healthy. If you're in the military and about to be sheep dipped, it means your life is about to get a whole lot more interesting. It's a term intelligence agencies use when they pretend to boot someone out of the military but secretly turn them into a covert operative.
Don't worry, you still get your military retirement time. You just can't tell anyone about it.
While "sheep dipping" isn't the official term for moving a troop from military service to the clandestine service, it's the term the Agency uses to describe the process of taking a career soldier, sailor, airman, or Marine out of their branch of service on the surface. Instead of really removing the subject, the intelligence agency will just pull their official records, leaving behind their official record, the one which says the troop is retired, separated, or otherwise not in the military anymore.
The agency will take care of your real official record from there but there's still work to be done on the service member's part. They will be establishing an entirely new identity for themselves, after all. Their job is to make the move plausible, writing to friends and family telling them why they got out, what they're going to do after leaving the military, and whatnot.
According to L. Fletcher Prouty, a retired Air Force Colonel who served as the chief of special operations in the Kennedy Administration, the practice started during the Vietnam War, when the Geneva Accords on the neutrality of Laos in 1962. This agreement prevented foreign combat troops from entering Laos. American troops, engaged in combat in neighboring Vietnam, were forced out of the country. The Nixon Administration, not known for honoring international borders when it came to prosecuting the war in Vietnam, decided they would need military support for intelligence agencies in Laos and opted to use "sheep dipping" as a means to get military members into the country.
If this seems implausible to you, remember we're talking about the guy who decided to bug the Democratic National Committee and then cover it up, even though he was about to win in the country's biggest landslide.
The North Vietnamese were secretly supporting Laotian Communists in their effort to topple the Lao government, so why shouldn't the United States do the same thing in order to support the Laotians? Besides, the NVA was still using Laos as a staging point for attacking allied troops in South Vietnam. The United States military decided to sheep dip a number of specially-trained U.S. troops in order to conduct a clandestine war in Laos. Nixon even allowed the Air Force to provide air support for the Secret War in Laos.
The sheep-dipped soldiers of Vietnam were all provided with their full pay and benefits, not to mention regular promotions and their retirement. If a sheep dipped troop were to be killed in the line of fire, that would pose more of a problem. Their family would struggle to get the benefits befitting a widow – but the agency handled each case separately.