Widow's Allowance
  
Ignoring for a second the gendered nature of the term, the idea behind the "widow's allowance" (or sometimes, in a more woke formulation, a "bereavement allowance") is that some amount of a dead person's estate will be released to their grieving spouse while the rest of the estate gets processed.
You and your spouse are getting up there in years. Your sig other dies, and it's going to take a few weeks for the lawyers to work out the estate and get you the money you're due as their heir. In the meantime, you have bills to pay: rent, utilities, the funeral, your new subscription to a geriatric dating site, etc.
The widow's allowance is an amount of money released from the estate immediately to allow you to pay these bills. Meanwhile, the legal gears will continue turning and (hopefully) you'll have access to the full estate soon. Which would be nice, because there's a divorced retired doctor who loves travel and long walks on the beach who's been messaging you.