1. What does it mean?
GG stands for good game and can be a sportsmanlike closing message. Korean gaming and casual speech also use 지지 or GG 치다 to mean conceding, giving up, or admitting a situation is beyond saving.
Also written or said as 지지, ㅈㅈ
2. The nuance
Timing changes the tone. After a match it may be polite; before the outcome is settled it can sound defeatist, sarcastic, or like taunting the other side.
3. Examples
“경기가 끝나고 서로 GG를 쳤어.”
After the match, we both typed 'GG.'
“문제가 너무 어려워서 오늘은 GG야.”
The problem's too hard; I'm calling it quits for today.
Sources
References support the meaning and usage. Example sentences are written for NoCapWiki.