World Trade Organisation trade post Brexit would mean that without a deal, we would fall back to W.T.O. rules. This means charging large tariffs (money charged on the cost of a good that is imported) on imports and other countries would charge high tariffs on our exports.
In a Free Trade arrangement, you start with high tariffs and then negotiate them down. We will take % off your coffee (imported into our country) if you take a % off our tea (imported into your country) say. This will make their coffee and our tea cheaper for consumers and so good for business.
Free trade agreements take years to agree and are very complicated. (e.g. Maybe the coffee country above can get tea from elsewhere and does not want to annoy them too much because of another trade agreement)
All trade is currently within WTO rules but all countries have agreements or aim to have agreements (still within the regulations of the WTO) to bring down tariffs.
Some Brexiters have told us not to worry because the UK will unilaterally lower all tariffs to zero.
Problems with that: 1) Market is flooded with cheap imports e.g. meat so British farmers either have to lower their standards to compete or be put out of business.
2) There will be no incentive for other countries (in trade negotiations) to lower their tariffs! There is a brilliant explanation by Jason Hunter in this video on this from 6 minutes 50 to 8 minutes 49.
There is more info and links on an earlier blog post: WTO Part 1.