A FIRE economy is one based on Finance, Insurance and Real Estate services.
'Finance, Insurance or Real Estate services' was Division H of the former Standard Industrial Classification (SIC) used by the US census bureau. The 'and' technically unites the NAIC codes 52 and 53 analogous to the SIC Division H.
SIC was replaced by the North American Industry Classification (NAIC) System.
FIRE was the largest industrial division in the New York economy. Journalists popularised the acronym in talking of New York's economy.
Other 'FIRE economies' may be London and, perhaps, Tokyo.
The FIRE economy is often compared pejoratively to manufacturing and export possibilities or perhaps the wider 'productive economy' of value added goods and (non-financial) services.