A visa (short for the Latin Carta visa, lit. "the document having been seen") is a permit given by a country that allows someone to go to that country. A visa is a document that is stamped on a person's passport by an embassy. It names the kind of visit and says how long the person can stay. Sometimes, people need to go through an interview held at the embassy before they get a visa.
Many countries require foreign visitors to have a valid passport and a visa before they can enter the country, but there are exceptions (see below for examples of such these).
Visas are associated with the request for permission to enter (or exit) a country, and are thus, for some countries, not the same as actual formal permission for an alien to enter and remain in the country.
Some countries, such as some states of the former Soviet Union, require that their citizens, and sometimes foreign travelers, obtain an exit visa in order to be allowed to leave the country. Until 2004, foreign students in Russia were issued only an entry visa on being accepted to University there and had to obtain an exit visa to return home. This policy has since been changed, and foreign students are now issued multiple entry (and exit) visas.