The golden handshake is a stipulation in a hiring contract which guarantees that the employer will provide a significant severance package if the employee loses their job. The package may include cash, stock options or other incentives such as extended medical benefits and so on.
This hefty severance package is most commonly offered to senior executives. Since such individuals often switch jobs on a regular basis, hopping from one prestigious position to another, the value of their name can be significant. However, because they move about so much they want to ensure that they leave a position in a financially beneficial position, since there may be a non-competition clause in their contract that keeps them out of work for a while.
Golden handshakes can amount to millions of dollars. They may be offered, even without being part of a contract, to encourage an employee to retire. When applied in this fashion they are more like a Golden Boot than a handshake. In this case retirement may not be optional, although you may end up with something to sweeten the experience.
If you are high enough on the corporate ladder to merit a golden handshake clause in your contract, read it carefully. There may be specific terms that require you to remain in your position for a minimum time period or that rescinds the offer if the company goes bankrupt. If you are being offered such an offer as incentive to retire, feel free to bargain for the best terms you can. Do so with care though, since the offer may be withdrawn if the company terms it too expensive.