1. What does it mean?
For media, 정주행 means following the episodes or installments from the start in sequence. It can describe a first viewing or a rewatch of a drama, webtoon, or other series.
Also written or said as 정주행하다, jeongjuhaeng
2. The nuance
It is often translated as 'binge-watching,' but the emphasis is on going through the series in order; it need not be completed in one sitting. The ordinary travel-related meaning is separate from this media use.
3. Examples
“앞부분을 잊어버려서 첫 권부터 다시 정주행하려고.”
I forgot the beginning, so I'm going to reread the series from volume one.
“퇴근 후 한 편씩 정주행 중이라 아직 결말은 몰라.”
I'm watching it in order, one episode after work each day, so I don't know the ending yet.
Sources
Financial News: Korean language in use
References support the meaning and usage. Example sentences are written for NoCapWiki.