Economic indicators are basically the most recent set of statistics that relate to be economy. This would include areas such as the current GDP, or perhaps the rate of unemployment, and other considerations such as the rate of inflation.
All of these indicate how well the economy of the country is performing. All of these statistics combine with other less specific information such as a threat of war, a huge oil leak, industrial unrest, and many other factors in indicating how well an economy of a country will do in the short or longer term.
Governments and stock markets, many different industries and individual companies, as well as a whole host of organisations analyse all of this information to decide, for example, what a companies value may be on the stock market, and whether to by or sell its shares based on this information.
If for example there is a threat of war shares in tourism businesses may fall, conversely the country that is under threat of war may be a major producer of a commodity, as such, investors may decide that there will be a shortage of this commodity and its price may increase dramatically on the open market.
High unemployment may indicate that on average people will have less money in their pocket to spend and this will decrease the amount of goods that manufacturers can sell, it may also indicate that companies are not performing well as they are either shedding staff or failing to take on new staff, which would suggest the power worried about their financial futures.