In economics, depression is a period of severe decline in a national or international economy, characterized by decreasing business activity, falling prices, and increasing unemployment. Sort of like a recession on steroids.
Contrast this with hyperinflation and stagflation.
The Great Depression was said to have started in the great stock market crash of 1929 (Black Thursday) but the seeds of it were planted during the heyday of monetary mismanagement in the 1920s. It lasted through much of the 1930s - the U.S. economy didn't really pick up until America mobilized for World War II.