Alternate Beneficiary
  
When you write a will, the beneficiary is the person who will receive your stuff when you die. ("Beneficiary" as in they will benefit by getting your stuff, though we're sure they will also be really sad that you had to die for them to get it.)
However, sometimes a beneficiary will turn down an inheritance for some reason. Maybe they just don't want your extensive collection of commemorative hubcaps ("Remember the Alamo every time you drive, with our Jim Bowie and William Travis decorative rims!"). Since you won't be around to pick someone else (remember: you're dead in this scenario), your will better have an alternate beneficiary listed.
This also comes up on insurance policies. Your main beneficiary might not be around when your life insurance policy pays off (this definition has turned out kinda morbid). If not, the policy would revert to whoever you have listed as an alternate beneficiary.