European superstate is a term mainly used to describe a potential result of the European Union's integration, though it could also be linked to other historical attempts to bring the continent together as one single national entity.
Along with this connotation is the implication of the loss of individual state's national identity with the replacement of one single homogeneous identity which groups such as UKIP argue is a goal which the EU is trying to achieve.
The term is often used in contrast to an idea of a Federal Europe which argues that is to accommodate other national identities with partial sovereignty being retained by individual member states, though often the terms are mistakenly used synonymously.
Many of the arguments for having such a sate would be that it would turn the entirety of Europe into the worlds most powerful superpower. I would have all the militaries of Europe combined giving it an army easily bigger the US's and thanks to Europe's large population for size and high GDP per capita it would help Europe's economy.