Ok so it's not your usual guns-tanks-drones variety war between the world's two largest economies (phew!), but it is affecting the lives of many people in both countries, with the effects also being felt across financial markets worldwide.
You might be surprised to hear that this dispute isn't really new at all. China has been accused of dumping and other unfair trade practices by many different countries for a few decades now, with the US being one of the biggest complainants throughout. Unfair trade practices usually involve making something cheaper and selling it into a foreign market at a price so low that local industries can't compete.
This "complaining" process usually takes place via the World Trade Order (WTO), a global body which was created in 1995 to mediate exactly these types of trade disputes and bring about peaceful solutions for all parties.
Enter Donald Trump
Trump, on the back of a successful populist 2016 election campaign which was focused on appealing to exactly the types of people who had lost their livelihoods due to Chinese competition (farmers and steel & aluminium workers, to name a few), decided to stop trying to solve these problems via the WTO, and start taking matters into his own hands, and tariffs were the policy tool of choice.
Tariffs? What's a Tariff? Simply put, tariffs increase the price of imported goods. For example, if the US decides to apply a 10% tariff on $100bn of Chinese imports, it will collect $10bn of tariff revenue and the imports will be 10% more expensive in the US market, helping domestic producers of the same goods compete in the domestic market thanks to the 10% price hike of whatever they are producing.
What's not so simple, however, is the end result - a world where both countries keep applying more and more tariffs, which usually ends with things becoming more expensive than they need to be for those who buy the end product - US and Chinese consumers (and often people in other countries, too).