A visa is a document that permits someone who is not a citizen of a country to enter that country for specific purposes. For example, if you wish to visit the Middle Eastern country of Jordan, you have to obtain a visa (usually at the airport upon arrival) before you can officially cross into the country. The visa that you get depends on your purpose for being in the country; for example, a student visa allows you to study for an extended amount of time, usually at a university, and a work visa will enable you to obtain employment. Many people obtain tourist visas, which are valid for a certain amount of time and do not allow for one to engage in study or work.
If you have an American passport, you can visit about three-quarters of the world's countries without a visa. As a rule of thumb, you should always check on visa requirements before making plans to travel. Some visas can be cumbersome and very restrictive, such as if you want to go to Iran. Other visas can be easily obtained, sometimes even at the airport, when you arrive at your destination.
However, some places do not require any visa at all. If you have a US passport, you can visit Norway (and most European countries) without any visa. The Norwegian island of Svalbard, located high up in the Arctic, is an entirely visa-free zone. While obtaining a visa to Iran can be extremely difficult, there is an Iranian island called Kish, which does not require a visa. However, leaving Kish to go to the mainland of Iran can be challenging if you do not already have a visa.
The Schengen Zone in Europe is a visa-free zone where people can travel freely across borders without having to obtain a visa. The Schengen countries are Iceland, Portugal, Spain, France, Belgium, Luxembourg, Switzerland, Liechtenstein, Italy, Slovenia, Austria, Hungary, Slovakia, the Czech Republic, Germany, the Netherlands, Denmark, Norway, Sweden, Finland, Estonia, Latvia, Lithuania, Poland, Hungary, and Greece. If you arrive in one of these countries and wish to travel to other Schengen countries, you do not have to present a visa upon arrival.
Ireland and the United Kingdom are not Schengen countries, but some agreements allow travelers to visit them from other Schengen countries. Additionally, there is an open border between Ireland and the United Kingdom.