Essentially "dead" money is money that you have paid or are obligated to pay to a player that has yet to be accounted for on the NFL books. For most players dead money is simply prorated money that is yet to be accounted for.
Basically what this means is the NFL treats a player like a depreciable asset like a company would. Every player is determined to have a shelf life of either the remaining length of the contract or 5 years, whichever is shorter. When signing bonus money is paid up front the value is spread out over deal. If a player receives $5 million and has a 5 year contract each year the team will take a $1 million expense or cap charge related to that bonus. If you decide to cut the player the money unaccounted for accelerates and is considered dead on the books. So if that player above is cut in the third year of his contract $3 million becomes the "dead money" cost.
The other type of dead money is guaranteed money that you are obligated to pay the player even if he is not on the team. That is what makes the Sanchez cut unbearable. If he is cut Woody has to cut him a check for $8.25 million dollars. That amount also immediately counts towards the salary cap.
When you trade a player the signing bonus "dead money" will count on your books but that second category transfers to another team which is why trading Sanchez is the only option the team has. If the Jets traded Sanchez and found a team willing to take on all of his salary his dead cap to the Jets is around 9 million. No team would pay him that much, but at least its a hope.
Mike Vick will cost the Eagles $4.2 million to trade or release. His actual salary for the year is $15.5 million but none of that is guaranteed if the Eagles cut him a day or two after the Super Bowl. A salary swap for the Jets and Eagles would not really work for the Jets. They need Vick to get cut and then to sign him to a cap friendly contract.