When you cross a border from one country into another, you'll need to show your identification papers and maybe a visa to the border patrol officials.
A border separates one thing from another, most famously countries. Sometimes neighboring countries have border disputes, if they don't think the lines were drawn fairly or if they don't get along. Borders can also be less official. You might want to plant a border of cabbages along your front walk, or you could sew a border of sequins along the edge of your collar. But you'd have to go easy on the sequins, as too many would "border on the garish."