You need your worm can-opener for this one The main advantages are those surrounding trade freedoms & employment practices. We trade all over the world but, members within the EU enjoy certain perks when it comes to payment terms for duty, for example. And if you want to go and work in an EU country, you don't have to apply for permits and visas justifying your existence etc... you can just get on a plane and get started. A lot of the advances in employment law have originated in the EU recently, improving the lot of workers probably more quickly than if it had been left to national governments. The British-supported expansion of the EU (until relatively recently) has meant that poorer countries are raising living standards and income levels. This is good for the UK because it means we have new markets opening up for our goods and services.
BUT.. There's a high price attached and practices are seen as wasteful. Because the EU is expanding and movement is easy, the cheap jobs that formerly went to our own unskilled labour are often taken up by those from overseas. There's a lot of unhappiness that EU law overrides British law in places - the 'sovereignty' issue. There's a lot of discontent that it is very undemocratic. (Did you vote for the current EU president and would you even know who they are?). And, because they were the founders, it does tend to gravitate towards the needs of France and Germany (who largely didn't support expansion and would have preferred it to remain a tight, exclusive club with them in charge!)
Not sure what would happen if we opted out. Euro-sceptics always point to non-EU, non-Euro countries saying that they seem to do just fine. My feeling is that there would be protectionist strategies employed making British goods and services less attractive.