The European Community (EC) is the 1st 'Pillar' of the European Union, an international organization founded on March 25, 1957 by the signing of the Treaty of Rome. It was originally called the European Economic Community (EEC), but the 'Economic' was removed from its name by the Maastricht Treaty in 1992.
The Community is broadly the original institution, and covers a wide range of policy areas where decisions are made collectively by Qualified Majority Voting (QMV). Along with the 2nd (Common Foreign and Security Policy) and 3rd (Police and Judicial Co-operation in Criminal Matters) Pillars, where member states maintain a veto over many policy decisions, the Community makes up the European Union.
For further historical details, see History of the European Union and European Union Law.