The law of large numbers postulates that as a sample size grows, the mean of the sample will get closer to the mean of the total population. For an insurance company insuring a life against the possibility of death, the more people who are insured, the higher the probability that the actual mean death rate will approximate the national mortality tables of life expectancy for men and women per age category.
The law of large numbers gives us an idea as to why insurance companies like to insure a large number of people. The larger the number of lives, houses, cars, boats, and so on that the companies insure, the more closely the claims from losses will be predictable based on a normal statistical distribution. This allows insurance companies to price policies for life insurance and casualty insurance appropriately so they have a predictable return on their assets.