There are a few words for "pair".
1. 켤레 - "pair", for socks, gloves, shoes, etc.
구두 한 켤레(a pair of shoes), 양말 두 켤레(two pairs of socks)
2. 쌍 - "couple", of people and animals. (sometimes used for inanimate things too, but it's rare).
남녀 한쌍(a couple), 비둘기 한 쌍(a pair of pigeons).
3. 짝 - "one" (refers to the individual member of a pair or a set).
젓가락 한 짝(one of a pair of chopstick), 젓가락 두 짝(a pair of chopsticks), 양말 한 짝(a single sock).
짝 also means "mate" or "buddy", but as a count word used with a number, it can only be used for inanimate things.
Here's some usages of 쌍 and 짝.
- 쌍을 짓다, 쌍을 이루다, 짝을 짓다, 짝을 이루다 - pair up.
- 쌍쌍이, 쌍쌍으로 - in pairs.
- 쌍쌍 파티 - a couple party.
- 짝짝이다 - (it's) a mismatching pair/set. 양말이 짝짝이다 - These are mismatching socks.
- 짝궁 - school buddy (especially in grade schools).
- ~기 짝이 없다 - matchless in some quality (usually bad). 딱하기 짝이 없다 - pitiful like I've never seen before.