One of the original suggested referendum questions was "Do you think that the United Kingdom should be a member of the European Union?" It was rejected in favour of "Should the United Kingdom remain a member of European Union" because "some participants in our research did not know that the United Kingdom is currently a member of the European Union."* If that wasn't evidence the referendum was a bad idea... * http://…
If you check the history of the European Union (https://en.wikipedia.org/wiki/History_of_the_European_Union) it is history of various agreements between an ever-changing set of member states. Eventually (1992) there is the Maastricht Treaty that creates called the European Union, but that has been amended various times. To complicate things there is also the European Economic Community (renamed to European Community) and member states are in/out of various important provisions of European governance such as the Euro or the Schengen Agreement (like the UK and Ireland). The Schengen Agreement I believe includes even some non-EU members.
So people googling for "What is the EU" isn't proof of stupidity in my book. They may haven been familiar with critical elements of the EU (which were the deciding factors for their vote) but want to understand the full implications of this historic vote.