Basic problems can be solved either by the free interaction of the individuals pursuing their own objectives as is done in the market or in a planned manner by some central authority like the government.
In a centrally planned economy, the government or the central authority plans all the important activities in the economy. All important decisions regarding production, exchange and consumption of goods and services are made by the government.
In a market economy, all economic activities are organised through the market. A market is a set of arrangements where economic agents can freely exchange their endowments or products with each other.