What are the advantages and disadvantages of a total knee replacement surgery for 87 year old woman in good health, but horrible arthritis?

Depends. Arthritis can be horrifically painful and disabling. If the patient is healthy enough and willing to accept some risks then surgery is recommended. Major risks assuming the surgery is done correctly include: infection, blood clots, heart attack, stroke and even death (these are rare but they can happen) major benefits are pain relief and major improvement in quality of life.
Many pros/some cons. The goal of tkr is to reduce pain in the knee. This will lead to improved function and quality of life. It will not create the knee you had when you were young but a functioning knee that is better than what you have now. Your function and health are more important factors than your age when assessing the ability to undergo a major surgery. Downsides are the risk of complications after surgery.
Pain relief. If your 87 years old and healthy, life is not over. I have many knee replacement patients active at tennis and golf in their 80's & 90's in naples. But painful arthritis can take this away from an 87 year old who has tried everything else to relieve their pain unsuccessfully. The advantage is they can get their independence back and enjoy life while reducing their pain & fear of falling.