Also called: CREATE STATISTICS, multivariate statistics
In plain English
Normally PostgreSQL studies each column on its own. Extended statistics, created with CREATE STATISTICS, tell it to study several columns together so it learns that they are related — for example that city and country move together.
Why it matters
Without it, the planner assumes columns are independent and multiplies their selectivities, badly under-counting correlated filters like city = 'Paris' AND country = 'France'. Extended statistics fix a whole class of join-order and row-estimate disasters on real-world schemas.