The idea is that while it punishes the citizens of the country doing the tariffs, it makes their local industry more competitive in the country. This can be used fairly or unfairly.

Take steel for example. Most countries consider it a strategic resource, the want/need to be producing it to guarantee a supply in case of war, supply issues etc. Another country might be able to sell it cheaper, but you want to ensure your country still produces it; put a tariff on it, so foreign steel costs as much as the local stuff, keeping them in business.

Europe put a tariff on Chinese cars, because China was subsidising their companies so they could flood Europe with unfairly cheap cars. (Although local companies dropped the ball too)

Trumps tariffs won't work as no one trusts that they will remain - he changes them on a whim, so no one can build out manufacturing to take advantage of them.