Trade tariffs are applied to imported goods as a protectionist measure to defend a local supplier from products produced overseas where labour costs, environmental protection, industrial standards and other overheads may be lower. In the eyes of the nation raising the tariffs, this is a necessary measure to protect their manufacturers from dumping, to “level the playing field”. Free trade agreements are set up between nations that wish to facilitate bilateral trade which they are confident is fair. Non-tariff barriers to trade are regulations that goods (and services) must satisfy to be acceptable in a given market. Brexit advocates are hoping that by generating many free trade agreements, the UK will be flooded with cheaper goods yet (one assumes) higher priced UK goods and services will be able to penetrate foreign markets due to being of a higher quality.
The US president has been very bellicose against international trade with the US, suggesting that the USA has got the short end of the stick in (all of) the trade agreements it has freely entered into over many years, with international partners. Presumably, this is because only Donald J Trump knows how to strike a deal. The US and other major Western economies do have some ground for complaint with certain nations, of course. The most obvious example is China which the US has accused recently of unfair practices over aluminium and steel exports to the USA. However, the US president is making the same kind of accusation against US allies such as the EU nations. The US is planning to raise aluminium and steel tariffs against all exporting nations.
Speaking at a press conference at the White House with the Swedish PM (Sweden is an EU state) the president noted:
"The European Union has been particularly tough on the United States. They make it almost impossible for us to do business with them.” He went on to suggest that any EU retaliation over his proposed 25% aluminium and steel tariffs would be met by a 25% tax hike on EU car exports to the US applied in a “loving, loving way”. He insisted that his plan would somehow win over foreign critics: "They'll like us better and they'll respect us more”. This remains to be seen. His guest, Stefan Lofven, was clearly sceptical: "I am convinced that increased tariffs will hurt us all in the long run."
The EU is keen to avoid a trade war with the US which it regards as unjustified and mutually harmful, but it has already identified 100 US imports that could be subjected to retaliatory measures if needed.