A border is an edge or boundary, most frequently of a country. The longest border between two countries is the United States-Canada border. They can be very complex with enclaves and exclaves, such as the India-Bangladesh border. Border disputes can simmer for decades, e.g. the Kashmir region divided between Pakistan and India.
The Armenia-Turkey border is an example of a closed border. 65 countries have built a wall on (some of) their borders. The best known walls are on the Israel-Palestine border, and on the United States-Mexico border (partially built at the moment).
Another phenomenon is open borders, where a number of countries agree to give full access to civilians and goods of other member states to enter their territory, e.g. the European Union. Donald Trump famously remarked that "A nation without borders isn't a nation".