A tariff is a tax the importing country charges on goods coming in from abroad. It's paid by the importer, a domestic company, not by the foreign exporter.
The importer almost always passes some of that cost to customers. So the shorthand 'foreign countries pay our tariffs' is, mechanically, not how it works.
Tariffs can protect specific industries or raise revenue. They can also raise consumer prices and invite retaliation. Whether they're worth it is a policy question. Who writes the check is not.