A Trade War is conflict between two or more countries using tariffs (similar to a tax) to help each country create a positive import/export balance.
Trade Wars may begin when one country places a tariff (like a tax) on a good that is imported into the country at a lower price than the same domestically produced good can be sold for. The tariff is used to balance an unfair trade practice with the goal to create benefit for the consumer by allowing the domestically produced good to be cheaper than the imported good. Once one country places tariffs of a certain goods, the second country affected by the tariff may retaliate by placing a tariff on a different set of goods that is imported into their country. Hence you have what many call the beginnings of a trade war.