The eurozone created the European Support Mechanism (ESM) which operates much like the International Monetary Fund (IMF). It collects funds from its member states, and it has been using those funds to recapitalize the banks in peripheral countries that are at risk of failure. The German Parliament passed a bill that authorizes Germany to contribute to the ESM. Euroskeptics, on the left and the right, oppose the bill. They requested Germany's highest court to rule on it. The court determined that the democratically elected Parliament had the right to determine Germany's contribution to the ESM.
German support for the ESM was essential. It could not function without support from Europe's largest economy. The European Central Bank (ECB) will also help out the stressed countries in the eurozone. It will purchase bonds from the stressed countries in order to keep the cost of servicing the debt manageable. Private investors in those bonds have demanded a risk premium that is unaffordable.
Markets across the world reacted positively to the decision by the German court. The euro also rose in value relative to the dollar. A negative decision by the German court would have been a serious blow the the euro and to the general movement toward European integration.