There is no single official definition. In the US a committee of the National Bureau of Economic Research dates recessions using many indicators, especially employment and income. Elsewhere, two consecutive quarters of falling real GDP is a widely used rule of thumb.
Why it matters
Recessions bring rising unemployment, falling profits and, usually, falling share prices and interest rates. Markets tend to fall before a recession is confirmed and recover before it ends, because prices look ahead.
See the data: US yield curve, US unemployment.
General information, not advice.