Borders are a figment of the state's imagination
Borders aren't natural or intrinsic. They separate geopolitical designations. Many of the borders today were devised and drawn by colonial powers. Sometimes, they're totally arbitrary.
Take the continent of Africa, for instance. During the colonial period, Britain, France, Belgium, and others decided where their areas of political influence began and ended. Those areas became the African nations we see today.
As a result of ill-informed map drawing based largely on resource availability, the designations split many African nations right down the middle (remember, a nation is composed of an ethnic or cultural group, not a geographic location). Today, when European hard political power has retreated, the result has been border conflict after border conflict as well as the creation of many unnecessary politically subjugated minorities. Usually, borders exist between nations (that is, people groups with different cultural identities), and are agreed upon between two nations.
The Berbers in North Africa provide a great example. They constitute an ethnic group that is so different from others in North Africa that it uses a totally different language (most of Northern Africa speaks French or Arabic). The Berbers exist between Morocco and Algeria, which split the group along random rivers or mountains into two different political entities. Should the Berbers create their own state, establish their own borders, and construct their own government? These questions lead down a rabbit hole of thought experiments regarding individual and collective property, right to self-determination, and cultural identity, but they're important to consider.
The border between North and South Korea, too, is an entirely arbitrary geopolitical designation on a latitude line created by cartographers. As is well known, the border is a result of an armistice that ended the fighting in the Korean War. North and South Koreans are ethnically (and back in the 1950s, culturally) homogeneous and sometimes members of the same family. Hopefully, these next few years will see a reunification of Korea.
The border along Gaza is imaginary as well. After the six-day war in 1967, the current location of the border between Gaza and Israel represented an armistice line. Israel erected fences and border security, claiming it as a legal border with Gaza. However, there was no ethnic or political reason for the border (besides the temporary armistice); it was, and is, almost purely arbitrary, and is used repressively to keep Palestinians contained within Gaza. Israel's population is 20% culturally Arab, many of whom 70 years ago occupied the same geographic locations as those in the Gaza strip.
In the United States, the (original) borders were drawn entirely by the kings and aristocrats of Britain. Whether through private or royal charter, the ruling power was allocated a certain area of land to own and develop. The idea that the British colonies ended at the Detroit River or North of Maine would have seemed crazy. Britain controlled many colonies in Canada at the time. In fact, American patriots made real efforts to retain Nova Scotia as a 14th colony. They even launched a propaganda campaign in Quebec that received sympathy and recruited many to the American cause. After the Americans lost in Canada and couldn't rally enough support, they included article XI in the Articles of Confederation which gave special privilege to Canadian colonies wishing to join the union:
Why is Nova Scotia considered foreign territory after the revolutionary war when it had so much in common with the other colonies? Because of geopolitical forces. Not anything real.
Today, the United States' southern border proves an interesting case. People along the border speak Spanish and exhibit a mix of Mexican and American culture. As it stands, the border separates geopolitical force as well as some cultural differences. As time goes on, the border will become meaningless as the cultures merge even closer.
Borders are simple, actually. They represent political designations where a state can use force to maintain its national identity by excluding others with different heritage. However, a border usually represents nothing more tangible than a line on a map and a fence, if that.