Most countries have rules and regulations around imported goods. For example, living here in the UK I cannot buy some guns in the USA and import them - I would need a licence from the government to do that. I cannot under any circumstances import heroin or cocaine. Where I can import goods they may be subject to an import tariff; this is basically a tax levied on imports, generally aimed at protecting domestic manufacturers.
A trade agreement is where two countries (or groups of countries) agree on what goods they can and cannot import/export between them, what regulations will apply (quantities, standards, etc) and what import tariffs will apply. When no tariffs apply, it's called free trade.
EU member states have free trade between them. So I can import widgets from Germany without being charged an import tariff. Similarly I can export the widgets I make to Germany without my customer being charged German import duty. It makes trade between countries easier and cheaper.
If we left the EU, the trade agreements that we have based on our EU membership would end. That means we would have to negotiate a trade agreement with the EU itself, and with non-EU countries that have trade agreements with the EU (e.g. USA).
Such negotiations would take a while to make. It is likely that there would be something of a mess while this was being done... The "Remain" camp are saying it would be economic Armageddon. The Brexiters say it wouldn't. What's the answer?
Fact: nobody knows.
The EU takes a lot of our imports. So we would want to negotiate a trade deal with them. The question is: what terms would we get? Norway, for example, is NOT an EU member, but has a free trade agreement with the EU. However, they have to follow most of the significant EU rules - and (I believe) pay EU membership fees! So they are not in the EU, but their trade agreement means that it they are not completely free agents.
So the knotty problem is what kind of trade deal would we get with the EU? The EU needs us (we take a lot of their exports) so they will want an agreement too. However, having just left the club they will not too happy with us and might play mean... What deal would be reached?
Fact: nobody knows.
This is an important subject, because our exports create our wealth. Wealth that we need to fund the NHS, education, etc. These social services move money around but do NOT create wealth.
Whatever either side may say, nobody knows what will happen. Economic armageddon or heaven on earth? It's anybody's guess.
My personal view is that there would be some chaos - perhaps even a mini-recession, but that things would have settled down after maybe 5 years and then we'd be fine.
It comes down to a simple question: do you think the UK has the skills, qualities and flair to succeed outside the EU?
The UK is the world's 5th largest economy. The EU as whole is 1st or 2nd.
So currently we're a big fish in a big pond. Would we be better off as a big fish in a huge pond?
EU membership benefits us - but could we benefit more outside?
There are no hard facts that can give an answer. It's a matter of belief.