The basic idea behind insurance is that a lot of people pay a little money into a fund that pays for the losses that any of those people might suffer. Self insurance is the creation of a fund from which an individual can pay for losses himself. Businesses are likely to be self insured against some risks but not against others; this is called risk-specific self insurance.
Most people are partially self-insured, although they may not realize it. Automobile insurance and health insurance have "deductible" clauses which mean that the individual pays part of the costs of repairing his car or caring for his health. Each person must decide how much risk to bear and how much he is willing to pay in premiums to have an insurance company bear the risk.
For a US citizen, a health savings account may be a good self insurance option. The health savings account is usually used along with a high deductible health insurance plan. In that way, the individual sets aside money to pay for his own ordinary healthcare while carrying insurance against major medical costs. An additional benefit is that payments into the plan are not subject to federal tax at the time they are made.
House insurance is another area where a person is usually partially self-insured. A homeowner may want to consider using a high deductible insurance plan, and putting the savings in premiums into the bank where they will earn interest but will still be available in case of fire or other catastrophe. The probability of fire or other claim may be so low that every few years the homeowner can use part of the savings while retaining enough to pay the deductible.
Automobile insurance has a wide range of coverages, and high deductible policies can save a driver quite a bit of money. If the likelihood of the car getting dented in a parking lot or on the street by someone who would just "hit and run" is high, a high deductible might not be the best plan. Even in this situation, however, the car owner may benefit by putting the premium difference into the bank, with the possibility of profiting on the amount of interest earned.
Business self insurance follows the same line of thinking, but can be considerably more complex. Large businesses tend to self insure more risks than small businesses. Usually a business will undertake self insurance only with the advice of an accountant and a risk management expert. Tax considerations can cause even a large business to purchase insurance rather than self insure for specific risks.