Hungary is part of the Schengen area, which comprises 27 countries that have chosen to allow the free movement of citizens without border controls. Those countries are: Austria, Belgium, Croatia, the Czech Republic, Denmark, Estonia, Finland, France, Germany, Greece, Hungary, Iceland, Italy, Latvia, Liechtenstein, Lithuania, Luxembourg, Malta, the Netherlands, Norway, Poland, Portugal, Slovakia, Slovenia, Hungary, Sweden and Switzerland. Countries in the Schengen area apply a common visa policy for short stays.
The European Union's External Action services has issued an FAQ document which should also answer most queries such as the single application procedure in case of travel in multiple Schengen countries. It is accessible on https://eeas.europa.eu/sites/eeas/files/frequently_asked_questions_en.pdf