A Dutch importer, for example, might place an order with a Spanish company. Payments to and from the accounts of the buyer and seller are channeled via central banks, so the Spanish exporter's bank gets a credit with the Banco de España, which in turn has a claim on the ECB. The Dutch importer's bank owes its local central bank, leaving De Nederlandsche Bank with a debit at the ECB.
The idea behind this was that the liabilities within the TARGET2 system would cancel each other out. To everybody's utmost surprise, however, this has not happened. For example, Germany is currently being owed over 650 billion Euros. Needless to say, the countries who owe this money don't have it anymore.