The major reason why the United Kingdom should remain in the European Union is because membership in the EU allows the UK to have unlimited access to the economies of other EU members. This helps the UK in a number of ways.
First of all, being in the EU means that British businesses can export their goods to all other member states without any of the sorts of barriers that are involved when they export to non-EU states. This makes exports much easier and helps the British economy.
The reverse of that is that imports are also easier to come by. Though some may say that this is bad (it hurts some British firms, for example), this ends up benefitting consumers in the UK because they can get the best possible combination of price and quality.
The ability to trade freely with the rest of the EU is the major benefit of EU membership for the UK.