Border has several different, but related meanings:

A border can be a margin around the edge of something, such as a lawn, garden, photograph, sheet of paper or even a country.
A hebaceous border is a narrow strip of plants along the edge of a garden path or a lawn or fence.
A thing can be said to be on the border if it lies in a grey area at the edge of a category or condition or borderline between two different situations but not clearly in one or the other.
Borders define geographic boundaries of political entities or legal juridictions, such as governments, states or countries. For the purpose of border control, airports and seaports are also treated as borders. Most countries have some form of border control to restrict or limit the movement of people, animals and goods into or out of the country. In order to cross borders people need passports and visas or other appropriate forms of identification. To stay or work within a country's borders an alien, or foreign person, may need special immigration documents or permits that authorise them to do so. Moving goods across a border often requires the payment of excise tax, which are often collected by customs officials. Animals moving across borders often need to be put in quarantine, to prevent the spread of exotic animal diseases. Most countries prohibit carrying illegal drug or endangered animals across their borders. Moving goods, animals or people, illegally across a border, without declaring them, seeking permission, or deliberately evading official inspection is known as smuggling.