The phrase "to require a visa" means that if you want to visit or enter a particular country, you need to have a special permission stamp in your passport called a visa. Full definition
It's also common for countries not to require a visa for short visits. (travelandleisure.com)
This travel resource makes my planning convenient as it clearly indicates countries whose government require a visa in advance. (mindthetravel.com)
Such a deal wouldn't be as attractive to people who would then require a visa to return to their native country, so there is motivation for them to negotiate such deals. (politics.stackexchange.com)