A broad, sustained decline in economic activity
A significant decline in activity spread across the economy, lasting more than a few months; dated after the fact by committees such as the NBER.
The popular definition is two consecutive quarters of falling GDP. The NBER, which dates US recessions, uses a broader judgement of depth, diffusion and duration across employment, income, production and sales. Its dates are the shaded bands on the US charts; the CEPR dates the euro area the same way, and the UK and Japan bands follow their national conventions.