A set of EU rules called the Dublin Regulation requires that asylum seekers--people asking to be declared refugees and granted the right to stay in the EU--apply for asylum in the first EU country they reach. This means huge numbers of applicants in Greece, Hungary and other countries in southern and eastern Europe. Those ports of entry are relatively poor and offer few government-funded benefits to refugees. Many migrants therefore want to go to Germany and other relatively wealthy countries in northern and western Europe. Some countries in northern and western Europe are welcoming the asylum seekers, most notably Germany, while others are trying to discourage them, such as Denmark. Indeed, Germany's non-enforcement of the Dublin Regulation and its relatively generous benefits to refugees may be contributing to the influx.
Important economic issues related to the crisis include: Are the migrants refugees or economic migrants? How do the policies of the EU or its member states affect the inflow of migrants? How should the EU and its member states respond?
Here's a great graphic on the current scale of the migration crisis in the EU. The United Nations High Commissioner on Refugees (UNHCR) has lots of information about the crisis. The EU is discussing whether to adopt quotas to distribute refugees across member states. The Common European Asylum System explains much of the EU rules regarding asylum seekers.