European Union - EU
The European Union is an economic community comprising most of Europe. Its main feature is a free market among its member states...no tariffs, no passports, free transport of goods across country borders.
It also represents a (relatively weak) political organization. The member countries remain sovereign nations, but there is a European Parliament, and the EU collects its own taxes, especially the so-called VAT tax. That name sounds like a Hungarian mispronouncing something ("that tax," perhaps), but it stands for "value-added tax" and works kind of like a sales tax.
Meanwhile, many EU countries also belong to the Eurozone, or the group of countries that use the Euro as their currency. However, there are a handful of countries that belong to the EU but don't use the euro.
The EU developed over a long period of time. It started in the 1950s with a series of relatively limited trade treaties (the first steps focused on steel and coal). In 1957, six Western European countries (France, Belgium, Italy, the Netherlands, West Germany, and Luxembourg...you never want to leave out Luxembourg) signed the Treaty of Rome, which set up the European Economic Community (later the European Community), a precursor to the EU.
The European Union itself was created by the Maastricht Treaty (sounds like a Hungarian sneezing), which took effect in 1993. The organization has been developing ever since, through a series of subsequent treaties and the joining of additional nations.
As of 2019, the EU comprised most of Europe west of Russia (which is not a member). Notable exceptions include Switzerland, Norway, and Ukraine, which aren't in the EU either. Some other countries are considered candidates for membership, but have not been accepted yet. This list includes nations like Serbia and Turkey.
And then there's the U.K. A long-time member of the EU, voters in the U.K. narrowly supported a special referendum to leave the pan-European economic zone in 2016. As of March 2019, the U.K. remains in the final negotiations (a nice way of saying "panicked flailings") to leave the EU.