Primarily a tracking and numbering system for tickets, bags, cargo etc.
Even non IATA airlines get assigned numbers if they ever plan to interline baggage and cargo, trace lost bags via established computer systems or get paid via the the airline clearing houses.
Many well know airlines have numbers assigned, however are not IATA members, in the US for instance Southwest, JetBlue, AirTran, Midwest Express, Hawaiian Air, Frontier are all non members of IATA. In addition some major airlines like Singapore and Korean Air have only joined in the last few decades, primarily as these airlines refused to take part in the IATA fare pricing requirements of the past.
From the desert to the sea, to all of Southern California