Wikipedia
The Eurosystem is the monetary authority of the eurozone, the collective of European Union member states that have adopted the euro as their sole official currency. The ECB has, under Article 16 of its Statute, the exclusive right to authorise the issuance of euro banknotes. Member states can issue euro coins, but the amount must be authorised by the ECB beforehand.
The Eurosystem consists of the European Central Bank and the national central banks (NCB) of the 19 member states that are part of the eurozone. The national central banks apply the monetary policy of the ECB. The primary objective of the Eurosystem is price stability. Secondary objectives are financial stability and financial integration. The mission statement of the Eurosystem says that the ECB and the national central banks jointly contribute to achieving the objectives.
The Eurosystem is independent. When performing Eurosystem-related tasks, neither the ECB, nor an NCB, nor any member of their decision-making bodies may seek or take instructions from any external body. The Community institutions and bodies and the governments of the member states may not seek to influence the members of the decision-making bodies of the ECB or of the NCBs in the performance of their tasks.
The Eurosystem is distinct from the European System of Central Banks (ESCB), which comprises the ECB and the central banks of all 28 European Union member states, including those which are not part of the eurozone.