According to Gavin Hewitt, Europe editor for BBC News, the concessions mean that:
[T]he eurozone’s bailout fund (backed by taxpayers’ money) will be taking a stake in failed banks.
Risk has been increased. German taxpayers have increased their liabilities. In future a bank crash will no longer fall on the shoulders of national treasuries but on the European Stability Mechanism (ESM), a fund to which Germany contributes the most.
In the short term, these measures will ease pressure in the markets. However there is currently only 500bn euros assigned to the ESM. That may get swallowed up quickly and the markets may demand more. It is still unclear just how deep the holes in the eurozone’s banks are.