It conveys the possessive. "Enemy's country" means "country of the enemy". "The car's wheels" = The wheels of the car "The dog's nose" = The nose of the dog "A person's possessions" = The possessions of a person

There's a subtle difference between "enemy's country" and "enemy country". "Enemy country" is a compound noun. The word 'enemy' tells us what kind of country it is. In the term "enemy's country", the word 'enemy' refers to a particular person or a group of people. An "enemy's country" is the country that this person or people come from. An "enemy's country" is the country of one's enemy. "Enemy country" means that the whole country is the enemy of another country.This isn't the case with "enemy's country". The person him/herself may be your enemy, but not necessarily the entire country.