ok, the Market Economy, which is adopted in many democratic countries, is based off of the ideology of supply and demand. The Market Economy has little government involvement and is a spontaneous kind of economy.
The Command Economy is used in Communistic Countries. The belief of this economy is that the government controls what is sold at what price and how much quantity of that product.
Traditional Economy is more what you would find at a local market or trade days. The main features of this economy is more or less like trading and bartering. Money is rarely used in this economy.