Here's a bit of random Korean trivia: all Koreans turn one year older on January 1st, not on their real birthdays. They still celebrate the birthdays but it's not as special as in other countries. The reason for the January 1st collective birthday (I imagine) is that Koreans need to use different politeness levels to older people and to people who are the same age as them. Imagine if someone was half a year older than you, you'd need to switch between these levels a lot, it would be confusing and difficult. So they decided that everyone born in the same year was the same age. Neat, huh
And yeah, they usually ask or offer their age when meeting new people because they need to know which politeness endings to use.