In trade, people exchange goods with each other. In the past, they exchanged one good directly for another, that was barter. Nowadays, people usually pay for goods with money.
When one speaks of "trade", one means all trade in a country or the world. Trade is a part of the economy. When something has been produced, trade is needed so that the producer can get his goods to the people and earn money with them. Also, customers want to be able to buy goods.
It is also said that a country trades. But the trader is usually not the country itself, the state, but the many companies in the country. China, the USA and Germany are the countries that trade most with other countries.