A micro-captive is a small captive insurance company, and the label usually signals one specific thing: the captive has made, or could make, the 831(b) tax election available to captives writing premium under the annual cap. Under that election the captive pays tax only on its investment income, not its underwriting profit.
Structurally there is nothing exotic about a micro-captive; it is a licensed insurance company like any other, just smaller. The name carries baggage because the election has been abused, and the IRS has litigated and won against arrangements that were tax products dressed as insurance. The distinction that matters is not size but substance: real risk, actuarial pricing, and claims actually paid. The 831(b) entry in the Tax section covers the election, its history, and when making it is worth deferring.