Trade wars are caused by countries trying to come in and rip off a design or product and make it cheaper than one country could make it.
Trump imposed the tariffs to China due to China ripping off products designed and created in the USA.
So they enforce that China pays Tariffs on products they make and import to the USA and they also pay Tariffs for things such as scrap metal that gets imported to China from the USA.
Customers in the USA pay those tariffs through higher product purchase prices and then the USA gets those tariffs which are actually taxes that are used to fund the government.
The Tariffs can help but the Tariffs can also hurt the economy and country.
Basically a Trade War starts when a nation attempts to protect its domestic industry and create jobs.