1. What does it mean?
A shortened expression for 혼자 하는 여행, a trip taken alone. It can describe a short local getaway as well as a longer journey; the defining feature is traveling without a companion.
Also written or said as 혼자 여행
2. The nuance
Solo travel does not mean avoiding every conversation or activity with others. The word concerns the trip's companionship, not a rule that you must remain isolated for its entire duration.
3. Examples
“이번 주말에는 가까운 바다로 혼행 갈 거야.”
This weekend, I'm taking a solo trip to the coast nearby.
“첫 혼행이라 일정을 너무 빡빡하게 잡지 않았어.”
It's my first solo trip, so I didn't pack the schedule too tightly.
Sources
National Institute of Korean Language
References support the meaning and usage. Example sentences are written for NoCapWiki.