Let's try examining tariffs in an attempt to decouple the idea from the current political polarization. I'll use a similar approach to examining minimum wage in my post Intellectual Vision.
Tariffs are a tax on goods or services from another country. A tariff schedule includes a detailed list of products along with tariff rates (% of value and/or a specific amount) and country of origin.
Raising Tariffs
If a country raises tariffs, the importer (not exporter) pays the fees. The importer can pay the fees out of profits or pass the costs onto customers. The customers may just agree to pay the extra costs or may decided not to buy the product. If they don't buy the product, they may be able to find another equivalent alternative. If they can find another alternative, it will most likely cost more than or not be the ideal fit of the import. If the alternative product is produced domestically, then these businesses can benefit from the additional demand and potentially increase production. Since this demand is essentially incentivized by the tariffs, the business is not experiencing competituve pressure to innovate or cut costs, potentially resulting in higher costs than necessary.
If the customers can't find an equivalent alternative, they will have to find a product that doesn't meet the same needs or may have to make due without the product.
The fees paid by the importer are collected by the government. These fees can be used by the government for productive manipulation of the economy, for example, by lowering taxes on consumers, offsetting the increased costs. These fees can also be used for non-productive applications, such as paying for excess government spending or special programs. In this case, the customer of the tariffed product ends up subsidizing the government program.
With complicated global supply chains, raising tariffs can end up hurting domestic producers that rely on foreign goods to make their products. Raising tariffs can have hidden costs such as creating an extra burden on businesses to adapt to changing rules.
Lowering Tariffs
After WWII, the U.S. lowered tariffs to promote global trade and economic recovery to help with post-war reconstruction.
If tariffs are lowered, a greater variety and quality of products can be found by consumers. Prices typically drop and global competition forces all suppliers to become more efficient. Foreign products may harm domestic suppliers if they can compete with cheaper foreign imports (due to cheaper labor or less regulation). Some domestic producers may benefit if they can by cheaper foreign parts for their products. If companies become dependent on foreign parts, this could result in supply chain disruptions, for example during a pandemic or war. If a domestic product is considered nationally strategic (e.g. defense, semiconductors), then lowering tariffs can put the national interests at risk.
With lower tariffs, a foreign government may reciprocate with lower tariffs. If they do, this may open new foreign markets for domestic producers.
An example of this is NAFTA (The North American Free Trade Agreement), where lower tariffs between the U.S., Mexico, and Canada resulted in generally lower prices on imports from the other countries, however many small Mexican corn farmers were put out of business as they couldn't compete with the large U.S. subsidized corn farms.
These last two examples bring up the issue of unfair trade practices, where a government can subsidize a product, then flood a foreign market with cheaper goods to destroy local industries. This can result in foreign monopolies taking over. This is the reasoning for high tariffs on many Chinese products.
Foreign governments may instead keep their tariffs high, creating an unfair trade balance.
Additional Thoughts
Reference:
https://en.wikipedia.org/wiki/History_of_tariffs_in_the_United_States