You see, but you do not observe. The distinction is clear. - Sherlock Holmes to Watson
Active or deep interpretation of maps is a subject that isn't taught nearly enough in schools, which is a bit of a pity as recognizing maps as clues to a country's character can give students an interest in geography they've never had before. Simply taking a good look at a map of a country compared to the other areas nearby is often enough to give one a good idea of what sort of geopolitical situation it happens to be in, and in many cases a good enough understanding of this can aid in even predicting the future between two or more countries.
Here are a few examples of some simple ways to read maps.
First of all, a perfectly straight border between countries. Sometimes that can denote friendship between two countries, where a certain latitude or longitude is set as a common border, after which there is no fighting over it.

It can also mean that the land between two countries simply isn't worth fighting over or too hard to manage. Here are a few examples from countries that border each other right in the middle of the Sahara Desert. Compare those borders to the much less straight ones up north - Tunisia, and Morocco. And after the Sahara ends in the south the borders become curvy again.

A generally straight border that nevertheless keeps twisting back and forth will usually mean a mountain range:

or a river (border of Mexico and Guatemala):

You can also tell quite a bit about a country's situation by geographical oddities. Take a look at this map:

Democratic Republic of the Congo is located mostly in the centre of the continent, but for some reason suddenly juts out to the west all the way to the ocean. Nations with access to the sea generally have it in a way not all that different from their other borders (a natural result of a nation's position), but when a large nation has a particularly tiny piece of access to the sea it usually means some sort of diplomatic resolution, without which it could have been landlocked. In Dem Rep Congo's case it was given this strip of land in 1885 by the
Berlin Conference.
Exclaves are also oddities. Kaliningrad is an obvious example.

Kaliningrad is part of Russia, but since the fall of the Soviet Union it has been an exclave completely surrounded by other countries, now the European Union. Supplies sent to Kaliningrad from Russia have to cross two borders - Latvia and Lithuania, Belarus and Lithuania, or Belarus and Poland.
The existence of an exclave can sometimes mean political instability if the host country is lacking in influence, as the geographic isolation alone can lead those living there to conclude that it would be better to separate.

The area enclosed by the red circle is an exclave of Angola called
Cabinda, where there was a conflict between the government and a secessionist movement there until a ceasefire was signed in 2006.
The same can be seen in areas of land that aren't technically exclaves but still a bit odd compared to the rest of the geography of a country. Looking a bit south you can see a strip of land stretching eastward from Namibia where you wouldn't normally expect its borders to extend.

That place is called Caprivi and unsurprisingly
there's a conflict there too between the country and a secessionist group.
The presence of a landlocked country where you wouldn't expect one will usually imply resentment or bad blood between one country and another. Take a look at Ethiopia:

You'll notice that Ethiopia one of the only countries in the area without access to the sea. Somalia has it, Kenya has it, Sudan has it...Ethiopia doesn't. The reason for that is the country located just to the north: Eritrea, which used to be a part of Ethiopia until it became independent in 1993 after 31 years of war with each other. Not surprisingly,
the two countries do not get along with each other.
Bolivia has a bit of a similar situation, though
the conflict that caused it was much less recent (19th century). Nevertheless, access to the sea is still blamed for a lot of problems in Bolivia and there is a
Day of the Sea celebrated each year in the country to remember the former coastline the country had.

There are dozens and dozens more ways to guess the geopolitical situation of a country through maps alone, but the above should suffice for now since the post has gotten a bit long (feel free to add your own in the comments below though). I'll end off with one more interesting one. Here's Indonesia:

Then Vanuatu:

And the Philippines.

What do they all have in common? They are all island countries, with a huge number of regional languages, but with one language that more or less unifies the country. Well, with the Philippines it's two (Tagalog and English). The reason for this is that it's simply impossible to manage a country of this type without a unifying language. Countries like Spain are usually able to get by with a number of languages with regional autonomy, but Vanuatu has 200 languages over a population of only a bit over 200,000, and administering this in the same manner would simply be impossible.
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