I'll try to explain (as an ordinary citizen - not a constituional expert).
The UK has a representative democracy which elects members to the House of Commons and a non-elected second chamber (House of Lords) which is supposed to act as a review/checking body. Many people do not like the non-elected part of this, but it is what it is. Both houses notionally advise the monarch who makes the law; these days it is a nicety and she basically rubber stamps everything but she is supposed to be a non-party-political figurehead.
Parliament = House of Commons + House of Lords. In other words all elected members of parliament [in the commons] and all memebers of the lords IRRESPECTIVE OF PARTY
Government = Ruling party (or coalition) - effectively whoever has the most seats in the commons.
The Government proposes laws but they have to be approved by Parliament as a whole; this puts a first level of check in the system unless one party has an overwhelming majority as there has to be appeal not only to the opposition but also moderate members of the ruling party.
For a few, specific cases the Queen can act without parliamentary sanction -- in reality this means that the Prime Minister (leader of the government/ruling party) can act without putting it to a parliamentary vote. After the recent wars in Iraq, Libya ... there is a groundswell of opinion to limit this prerogative.
Now what's happened with Brexit is that there was a referendum. Under UK constitution a referendum is only advisory and there to inform parliament (though in reality it directs action as going against the will of the people is not a good idea). In this case the margin was very close and there have been people calling foul (esp. as one of the campaign promises, widely advertised was reneged upon the day after the count).
David Cameron, the Prime Minister at the time, said he would stand by the result; he's since cut and run. We now have a PM that nobody has voted for (and who is introducing things not in the election manifesto). This is seen as a democratic deficit by many.
Many MPs are remainers, many people are having second thoughts and a lot of people are complaining that the terms of the exit were never spelt out before the vote.
The exit terms are to be negotiated. The current government do not want parliament to have a vote. This has been challenged in court.
One of the big ironies was that a key feature in the debate was to move from "unelected rule and lack of parliamentary sovereignty" -- and now the same people are fighting against these principles in court.
In short - it's a typical British cock-up. We lead the world in muddle and confusion; meanwhile the economy is going down the pan through all of the uncertainty.
âoeThe best argument against democracy is a five-minute conversation with the average voter.â â Winston S. Churchill