Over the decades the concept of Europe as a political entity has morphed from the European Economic Area (EEA) to the European Economic Community (EEC) to the European Union (EU).
Many people within the UK decided they had had enough of the rules being imposed from unelected bureaucrats within the EU and pushed for a referendum on whether or not we should leave the EU. David Cameron, the Prime Minister at the time (the PM is reasonably comparable to the President in the US) listened to the demands and called a referendum. The campaigning from both sides was of very low quality and driven largely by fear. The Remain campaign did little more than list establishment figures who favored remaining while the Leave campaign was a hotchpotch of people who wanted anything from control over immigration to economic freedom to just wanting to change something. The referendum was looking for a simple majority and, as with so many other elections these days, the result was close (52% voted Leave, 48% voted Remain). Not exactly a crushing mandate but a majority is a majority so Brexit it was.
With that in mind the UK filed notice to leave the EU. That started a 2-year period during which the UK and EU would negotiate the terms of departure. If no deal could be reached within the two years the potential outcome is what is referred to as a "no-deal Brexit", which essentially means that our relationship with the EU just stops. Part of the problem is that the current Prime Minister (Theresa May) supported the Remain campaign but has been tasked with negotiating the exit that she doesn't believe in. The EU wants to punish the UK because if it's too easy the fear is that other nations will also want to leave and the European project will be in tatters. Not surprisingly the result is a deal that nobody cares for, hence it was heavily defeated in a recent vote in Parliament (the defeat was the most severe in 100 years or more and bad enough to trigger a motion of no confidence in the government). A complicating factor is that the leader of the Opposition appears to want little more than as much chaos as possible because it may be his only chance to get elected.
Part of the problem is that much of what has been blamed on "Europe" has been the kind of policy that leaves the average working person bashed and battered at every turn. A lax immigration policy works well for companies as it helps keep wages down but at the same time it hurts working people because it not only puts downward pressure on wages but upward pressure on housing. And then there's the difference in how different parts of the UK voted. Just about every part of London voted to remain but with a few notable exceptions the vast majority of England voted to leave. Most of Scotland voted to remain. Of course whether the freedom of movement within the EU is a good thing will depend on where you are and your outlook. If you are a London-based architect or investment banker, the chance to bid on work across Europe is a good thing. If you are an electrician in Manchester the chances are you don't want to bid on rewiring someone's house in Barcelona, and yet the rate you can charge will be constantly under pressure because the electrician from Warsaw is willing to work for much less than you are. He's probably not in it for the long haul, he just wants to save as much as he can, as fast as he can, before going back home to Poland with enough money to be rich for the rest of his life. In the meantime he'll probably put you out of work.
The two year period to negotiate the departure deal ends in March. It recently transpired that the UK can cancel its notice to leave without reference to other member states. I believe the UK can also extend the negotiation period, although that may be simply by virtue of cancelling the notice to leave and immediately filing notice to leave, kicking off another two-year period.
It seems to be a big game of brinkmanship. When the EU responded to a crushing rejection of the deal on offer with little more than an insistence that there was no more room to negotiate it's hard to know what they expected.
A major sticking point in the whole thing has been the question of Ireland. Although Ireland is one island it is divided into the Republic of Ireland and Northern Ireland. Northern Ireland is part of the United Kingdom. During the 1970s and 80s we had "the troubles" where the IRA conducted assorted bombing campaigns on the UK mainland to try and create a united Ireland. With the UK being part of the EU there is no hard border between the two halves of Ireland, and the people of Ireland (on both sides of the border) seem to want that to continue to be the case. But if the UK ceases to be part of the EU the question is what kind of border controls are necessary. The people of Ireland don't want a hard border, but creating a notional border in the Irish Sea means that passage from Northern Ireland into the UK mainland means crossing a border, with border controls and all that entails. For a loose comparison, imagine if you could drive from Washington State through Canada and into Alaska with no border controls, but couldn't get from Washington to Idaho without showing your passport.
Since the project that is Europe has been ongoing for decades, much of UK law is closely tied to EU law, so unravelling it is a long and complicated process. Then there is the question of what happens to EU citizens who are settled in the UK as long-term (lawful) residents, and what happens to British citizens who are settled in other EU nations. Logically there is no reason to terminate their lawful residence but as soon as politicians start trying to act tough you never know what will happen.
Some have argued, quite reasonably in my opinion, that the UK voting for Brexit was in many ways like the US voting for Donald Trump. Whether people actually wanted that particular outcome may have been less important than a growing desire among the population to kick the establishment and try something, anything, different. It might be a leap into the unknown with all the risks that entails but when enough people figure "anything is better than this, I'll take my chances" the outcome may not be smooth sailing.
