The European Parliament has no powers in the EU.
The European Parliament is not allowed to adopt or decide anything, but only has an advisory function. Policy in the European Union is not decided by the EU Parliament, but by the Commissioners in the EU Commission, who are appointed or dismissed by the EU President.
In fact, not much would change if we had no EU Parliament. It is a representative body. It used to be possible to do without a directly elected parliament and the EU could continue to exist without it.
Recurrent pro-Kremlin narrative questioning the EU institutions' legitimacy and powers and seeking to discourage voter turnout in elections.
The European Parliament is a directly-elected institution. Since 1979, it has been elected by EU voters every 5 years. The last elections were in May 2014.
The European Parliament is one of the EU's two law-making bodies. It has constitutional-type and ratification powers. It passes EU laws, together with the Council of the EU, based on European Commission proposals. It has budgetary powers, scrutiny over the executive, hears citizens’ petitions, and appoints the European Ombudsman. A detailed overview of the European Parliament’s role in the European decision-making process can be consulted here.
As EU co-operation evolved with time, the European Parliament progressed from a purely advisory role to one of co-decision on an equal footing with the Council. The Lisbon Treaty expanded the number of policies which are subject to ordinary legislative procedure to virtually all areas including the areas of freedom, security and justice, external trade, environmental policy and the common agricultural policy.