Why it matters . . .
1. If we move to a position whereby the UK is taxing everything arriving from France at Dover, and similarly France is taxing everything arriving from the UK at Calais, the system won't work if goods can be brought into, or exported out of, a backdoor route across the Irish border. So if there's no customs union there would need to be a 'hard' border (i.e. with a fence or similar) between Northern Ireland and the Republic, with customs posts on either side to check what everyone has got in their cars. Given that some roads wind in and out of the two countries every few miles, and there are even some homes which actually straddle the border, that wouldn't be easy to manage (and it certainly wouldn't be popular with those people whose jobs and other commitments mean that they have to cross the border several times per day).
2. If, say, Japanese car firms make their cars in Japan, they'll face hefty import tariffs if they want to sell them in the EU (making teir models uncompetitive). So some companies have opened factories in the UK in order to be able to supply cars to France, Germany, etc, without having to pay import tariffs. If the customs union goes then those Japanese car firms will have to pay import taxes to get their cars into the rest of the EU, meaning that they might well decide to shift their factories to the other side of the channel (causing big job losses in the areas where they'd been making their cars here) in order to avoid paying those taxes.