As an example, try ordering cotton-based clothing from the USA. When the postman delivers it, you'll get charged 27% Import Tax (as well as 20% VAT and an £8 administration fee).
If you order a similar item from China, you'll pay 12% Import Duty (plus the VAT and admin fee).
However if you import it from France, Germany, Italy or anywhere else within the EU you won't pay a penny in Import Duty. (VAT will have been included in the purchase price anyway).
Basically, all countries tax imports of most items unless they've entered into agreements with other countries (either on a bilateral basis or, more commonly, as part of a 'free trade' area). The USA, Canada and Mexico have such an agreement (NAFTA), so that most goods and services can be traded freely across their borders. India, Bangladesh, Sri Lanka, China, South Korea and Laos have a broadly similar agreement (APTA). Such agreements show that even major trading powers (such as the USA and China) are reluctant to 'go it alone', believing that they're better off working in partnership with other nations.
The UK is in the European Economic Area, which provides 'barrier-free' trade across all 31 member countries, 28 of which are within the European Union.
If the UK was to leave to EU it could still remain within the EEA, so the UK could still benefit from free trade across the whole of the area. (Norway already holds such a status, as a member of the EEA but not of the EU). The disadvantage though would be that the UK would still be bound by nearly all EU rules, since they apply throughout the EEA, (which wouldn't please Eurosceptics) but with no say whatsoever as to what those rules should be (which wouldn't please the Europhiles).
If the UK was to leave both the EU and the EEA, treading with other European countries would be much, much harder and overseas investors (such as Japanese car manufacturers with plants in the UK) would almost certainly pull their operations out of this country.