This is a post about placenames because I find these kinds of things interesting. Fill in any blanks or make corrections if you can.
For whatever reason, Korea likes to refer to a connection (usually a railway or road) between two places by taking the first part of each word and combining them. When one of those places is Seoul, the syllable used is gyeong - for example Gyeongbu to refer to a rail line between Seoul and Busan, or Gyeongin to refer to the collective area/connection of Seoul and Incheon. Gyeonggi-do, the province surrounding the capital, literally means that. But why is "gyeong" used in place of "Seoul" or "Seo"?
Seoul is, as far as I know, the only native Korean placename in use. Everywhere else has over the course of history been converted to a Sino-Korean name, which can be written using Hanja (Chinese characters). For some places, the old native Korean name is still known, but is never used.
Seoul as a word simply means the capital. It's a word that has transformed from being a general noun (e.g., "the seoul of England is London") to being a proper noun referring to the city of Seoul. (Aside: I think 수도 is now the term to refer to a capital in general sense).
Seoul only became known as Seoul following the end of Japanese occupation. Prior to that, it had a few different (Sino-Korean) names, most recently Gyeongseong - a Sino-Korean word meaning capital city (gyeong/경/京 means "capital". When Seoul Station was built, it originally took the name Gyeongseong Station. So it makes sense that when they named the railway line between Seoul and Busan, they called it the Gyeong-Bu line, right?
So when you see 경 in relation to Seoul, you might have a skight appreciation of why it's there. But just because you see it, it might not be related. For example, Gyeongnam province or Gyeongju city both have "gyeong" but have a different Hanja and a different, totally unrelated, underlying meaning.