A quick glance at the pocket guide to Actuarial Tables & Life Expectancies shows that an old man is supposed to die, on average, within five years. So, you go to the old man and say, "Hey, I'm willing to buy your life insurance policy from you for $500,000 paid immediately."
From your viewpoint, this is a good investment. If he cashes it in by 70 as predicted, then you get paid $1 million on the policy, meaning that you've made $500,000 over 5 years, less any premiums you have to make to keep the policy up. In round numbers, this is a $100,000 per year pre-tax profit on your original $500,000 investment. That 20% annual pretax return doesn't look too shabby against current interest rates, and the insurance company is arguably much more solvent than any bank. Even if the old guy lives to 75, it's still not a bad investment, since then you're still making 10% per year. And the odds of the old codger living past 75 are somewhat offset by your hope that he will cash it in before 70 meaning that you made a great nice profit.
Most investors in life settlements are large financial firms and hedge funds who are looking for something that has at least the safety of high-grade corporate bonds, but with a high return. These firms buy many life settlements and pool them together. While these firms cannot predict is when a particular old codger will finally kick the bucket, they can employ the Law of Large Numbers to get a pretty good actuarial feel for when most of the policies will pay, thus allowing them to calculate their expected yield for the pool - and sell slices of the pool to investors looking for safe, higher yielding investments.
So, let's say that you have a $300,000 life insurance policy, your oncologist tells you that at best you have two years to live, and so the investors pay you $200,000 for it and you name them the beneficiaries of the policy. If in fact you die in two years, the investors will have made a profit of $100,000 split over two years, or what amounts to a $50,000 per year return - although this will be a pre-tax profit and income taxes will be owed on it.
This type of investment in the life insurance owned by a person who is probably soon going to die is known as a "viatical settlement". In the 1980s, an overnight multi-billion industry sprang up in investing in the life insurance policies of AIDS patients. This spread to cover terminal patients where certain death was a soon-to-be-realized certainty.