As one example, Japanese car firms have to pay hefty import duties if they build their cars in Japan and then export them to EU countries (making their cars harder to sell because they'll be more expensive than locally built cars).
So some of them have set up factories in the UK so that they can send their cars to France, Germany, Spain, The Netherlands, etc without having to pay import duties. (There are no import duties when goods are moved within the EU).
If the UK leaves the EU, those car firms will then have to pay import duties when the send their cars to mainland Europe, meaning that they'll be disadvantaged by having their factories here.
So those car manufacturers are likely to close their UK plants, resulting in big job losses among both their own employees and within companies who supply goods and services to those factories. That will mean that there will be some areas of the UK (which are currently reliant on car manufacturing to provide lots of jobs) where unemployment will be high. That then has a knock-on effect for other businesses, as fewer people will be visiting pubs, restaurants, cinemas, etc and High Street sales will also fall. That, in turn, will result in further job losses when those businesses either close down or simply cut back on staff.
Further, other companies based outside the EU (for example in the USA or, particularly, in China) will no longer have any incentive to invest in the UK, as they'll face hefty import tariffs when they try to sell their goods to customers in EU countries.
So the problem isn't (solely) about our own trading relationship with the EU but about how companies based outside of the EU will see the benefits or disadvantages of investing money in building plants within the UK.