I first learned about this years ago when I lived in Ireland. My wife and I were friends with a Korean family that was also working in Ireland, and their kids were similar age to my daughter.
My daughter was born in late, late December (just before New Year’s Eve), and is 5 years old in American culture. However, in Korean culture, she is 7 years old. What’s going on?
Sun Hyunwoo (also mentioned here) does a great job explaining this in this video:
To recap, Korean age, or hanguk nai (한국나이), starts with year 1 instead of year 0. Part of this is because the baby is in the womb for 9 months anyway, so by the time they are born, they have lived almost 1 year anyway. Also, Korean age marks the you are born into, rather than 365 days from your birth. So, at the end of the year, everyone becomes 1 year old according to traditional Korean counting.
So, going back to my daughter, when she was born, she was 1 year old. Then, a few days later, she turned 2 years old because the year changed. Thus, she is 7, not 5 according to the traditional Korean counting.
Also, when counting Korean years, you use the native Korean numbers because you’re counting something sequential. Since I am 34 in American age, but 36 in Korean age (I was also born very late in the year), my age is seorun daseot sal (서른다섯살) where “sal” means “years old”. It’s analogous to sai (歳・才) in Japanese I think. However, as TTMIK and others have explained, once you go past 40 years old, it’s too hard to remember the native Korean numbers, so people often switch to the Sino-Korean numbers instead. Thanks to “Keith” at Seoulistic.com for that advice.