1. What does it mean?
Repeated ㅋ letters represent laughter in text. ㅋㅋ can react to a joke or give a sentence a playful tone; longer strings are a stylistic way to make the reaction bigger.
Also written or said as ㅋㅋㅋ, ㅋㅋㅋㅋ, 크크, keukeu
2. The nuance
It does not prove that the sender is literally laughing. A short ㅋ or laughter after a criticism can also feel sarcastic. There is no universal character count that determines how friendly or amused somebody is.
3. Examples
“고양이가 자기 사진에 하트를 눌렀어 ㅋㅋ”
The cat liked its own photo, haha.
“다른 양말 신고 나왔네 ㅋㅋ 집에 가서 갈아 신어야겠다.”
I came out wearing mismatched socks, lol. I'll change them when I get home.
Sources
KoreanClass101: Korean language lessons
References support the meaning and usage. Example sentences are written for NoCapWiki.