In international age, after 1 year you were born you turn 1 year old.
But in Korean age, you become 1 year old at the moment you were born, and all babies born in the same year turn to next year old at the same time no matter which months they were born.
So, for example, if you were born December 31st, you become 1 year old for the day, and the next day, January 1st, you become 2 years old, even though you were technically "2 days" old. In more extreme example, if you were born at 11:59 PM on December 31st, you become 1 year old, and 1 minute later, which is 12:00 on January 1st, you become 2 years old even when you are technically "1 minute and 1 second" old.

And all babies born on January 1st to December 31st in the same year have all the same age by year basis, and they turn to their next age on 1st January every year at the same, no matter which months they were born.

 So, international age is rather based on relative calculation while Korean age is rather based on absolute calculation.

There might be some reasons why Korean age calculation method is like this:

1) First, we count the periods when you were in your mom's body as an unborn baby as 1 year old. It means that we consider the unborn baby as one living creature already.

2) Secondly, making a definition of who’s older or younger than me or the same age as me in personal relationship is important in Korean society. So we need uniform and standard one methodology to calculate age, and it is with respect to the point of control and regulation rather than with respect with each individual.

Korean language has generally big two ways of saying: one is honorific/formal language (존댓말) and casual language (반말), and what to use is totally depending on the ages in general, position at work, class year/grade at school, etc. So, in a class at school, if their ages are all different among classmates, it causes confusion of this social order. So, all classmates in one class at school need to be the same age to call each other friends.

Korea is affected by Chinese 유교 (Confucianism) historically. It is a philosophy about a way of governing or life. It started from a philosophy and became like a religion in Korea. The 유교 highly regard an order and rule between people according to their ages and class of society. But I think there are some aspects that this 유교 philosophy have turned into authoritarianism in Korea. So, people care about their ages and who’s older or younger than me.