Simple example: if UK leaves without agreements and treaties then there can be no flights from the UK to the EU. This sounds crazy but we have tens of thousands of bilateral agreements that drive even the most fundamental things, and they can be (and are) affected by e.g. the EU membership.
Or UK citizens would not be able to buy products from the EU because there would be no agreements in place that'd allow companies in the EU to export goods. Yeah, as soon as you BMW breaks down that's it, because no spare parts would be available.
Yes, it's this important.