The 12 golden stars that make up a circle on a blue background symbolise the unity of the European people.
The EU has used the flag since 1986. Although the EU had exactly 12 Member States in 1986, the number of stars has nothing to do with the number of Member States in the EU. The number of stars is fixed without regard to the number of Member States, since the number twelve is traditionally the symbol of perfection and unity.
It was originally the Council of Europe that chose the flag as a symbol in 1955. Today, the flag is used as a symbol for both the EU and the Council of Europe, even though they are two different organisations.