A 1910 law, still in force at 25 U.S.C. 47, that lets two buyers reserve contracts for Indian-owned businesses: Indian Affairs at the Interior Department, and the Indian Health Service at Health and Human Services. No other agency uses it, so you will only meet it in notices from those two.
Qualifying means combined ownership by Indians or federally recognized tribes of at least 51 percent, at least 51 percent of the contract earnings going to those owners, and daily operations run by an Indian owner who has real management or technical capability in the work being bought. Unlike 8(a) or HUBZone, there is no SBA certificate to hold: you self-certify on each solicitation, which makes it faster to use and more consequential to get wrong.
Two versions appear in notices. An Indian Economic Enterprise set-aside is open to any qualifying Indian-owned firm. An Indian Small Business Economic Enterprise set-aside, often written ISBEE, adds the requirement that you also be small under the SBA size standard for that NAICS code. Contracting officers give ISBEE priority at every dollar value, so the small-business version is the one you will see most.
In a sentence
"This acquisition is set aside for Indian Small Business Economic Enterprises under the Buy Indian Act." Only firms that are at least 51 percent Indian-owned and small for that code may bid, and a quote from anyone else gets rejected rather than scored.