I was watching a Kpop group answer some questions and one of the questions they got was “what do you want to do this year?” Their answer was to meet their fans (팬 만나기). So what purpose does the 기 serve here?
기 at the end of a verb creates a noun form of the verb, like the gerund ('-ing') in English.
팬(을) 만난다 = I meet fans. (-ㄴ다: present tense sentence ending form)
팬(을) 만나기 = meeting fans. (-기: suffix creating a noun form)
(subject/object particles are usually not included in this type of phrasing)
There are altogether three ways to create a noun form.
-기: suitable for well defined activities, like hobbies and other things. e.g. 수영하기** (swimming), 음악 듣기 (listening to music).
-는 것: most general way. Can create noun forms of unusual or infrequent cases.
e.g. 그렇게 말하는 것 (saying things that way), 빌린 돈을 안 갚는 것 (not paying back money you owe).
-(으)ㅁ: certain expressions, abstract concepts, literary contexts, etc.
e.g. 믿음 (believing, faith), 죽음 (dying, death). 기온이 상승함에 따라 생기는 현상 (phenomena arising from the temperature increasing)