The first thing to clarify is that the EU is not as big as you might have been led to believe — the European Commission employs fewer people than Edinburgh and Glasgow City Councils, but serves 500 million people rather than 1 million. There are 705 MEPs, but that is 76 fewer than there are members of the House of Lords, just one chamber of one member state Parliament (and MEPs are democratically elected). Yes, there is a lot going on in Brussels, but it is not that complicated.
Central to explaining how the various institutions work is understanding that the EU is not – in structure or intent – a federal country like the USA. At its heart are a collection of sovereign member states who came together to form a single market.
A single market needs rules to function and defining what things are means that trade can be conducted fairly and without discriminating against any individual citizen. Likewise, for Scots and other EU citizens to take up their rights to travel, study, live, work or retire in any other member state, we need to do that on the basis of laws.
If there is not agreement between the MEPs and the other EU institutions, the law doesn’t happen. The withdrawal agreement requireD the approval of both a qualified majority of the Council and a majority of MEPs.
There are four main parts to the EU: