On January 1, 1999, the European Union introduced its new currency, the euro. Originally, the euro was an overarching currency used for exchange between countries within the union, while people within each nation continued to use their own currencies. Within three years, however, the euro was established as an everyday currency and replaced the domestic currencies of many member states. Although the euro is still not universally adopted by all the EU members as the main currency, most of the holdouts peg their currency in some way against it.
The euro provided several economic advantages to the citizen of the EU. Travel was made easier by removing the need for exchanging money, and more importantly, the currency risks were removed from European trade. Now a European citizen can easily identify the best price for a product from any company in member nations without first running each price through a currency converter. This makes prices across the EU transparent and increases the competition between members. Labor and goods can flow more easily across borders to where they are needed, making the whole union work more efficiently.
The biggest benefit of the euro is that it is managed by the European Central Bank. The ECB has to balance the needs of all the member nations and therefore is more insulated from political pressure to inflate or manipulate the currency to meet any one nation's needs.
Of course, the euro is not without controversy. Many smaller member nations believe the system is tilted in the favor of large nations. While this may be true, the benefits of being an EU member outweigh the negatives, and there is no shortage of nations seeking membership.
The problem before the euro, as illustrated specifically with the European Exchange Rate Mechanism meltdown, was countries altering their own currencies to meet short-term economic needs – while still expecting foreign nations to honor the increasing unrealistic exchange rates. The euro has removed much, but not all, of the politics from the European currency markets, making it easier for trade to grow.
This question was answered by Andrew Beattie.