Self-insurance is the practice of retaining a risk rather than transferring it to an insurer. In personal financial planning it describes any deliberate choice to absorb a potential loss out of your own resources: carrying a $2,500 deductible instead of a $500 one, declining collision coverage on a car worth little, skipping an extended warranty, or simply accepting that a three-thousand-dollar repair will be paid from savings when it arrives. Insurance is the transfer of a risk for a price, and self-insurance is the decision that the price is not worth paying.
The phrase is worth pinning down, because it names three different things and only one of them is a household decision. This is the planning-profession usage, which describes a household's own risk-management choice rather than a regulatory status. The second meaning is a self-funded or self-insured employer health plan, in which an employer pays claims out of its own funds rather than buying coverage, typically with stop-loss protection behind it and largely outside state insurance regulation because ERISA governs it; the tax regulations use exactly that vocabulary, at 26 CFR 1.105-11, "Self-insured medical reimbursement plan." The third is statutory self-insurance, a regulated status a business qualifies for by demonstrating financial responsibility instead of buying a policy, which comes with net-worth tests, reserves and approvals. Federal contractors, for example, must submit a proposed self-insurance program to a contracting officer and obtain approval when the amounts involved are large enough (48 CFR 28.308), and underground storage tank owners can satisfy their obligations through a financial test (40 CFR 280.95). Neither of the last two is available to, or relevant to, an individual.