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Not as a burden, luggage, etc. I noticed it as a way of a king/emperor to refer someone, does it mean to refer it as himself or the other person he talk to?

Yes. 朕. A first-person singular pronoun for an emperor. Something like a majestic plural in English.

In Imperial China and every monarchy within its cultural orbit (including Japan, Korea, and Vietnam), the majestic imperial pronoun was expressed by the character zhèn (朕) (Old Chinese: *lrəmʔ). This was in fact the former Chinese first-person singular pronoun (that is, “I.”). However, following his unification of China, the emperor Shi Huangdi arrogated it entirely for his personal use. All other speakers and writers were obliged to choose some deferential epithet (such as yú (愚), “this foolish one.”) instead of using the former pronoun. While this practice did not affect the non-Chinese countries as much since their variants of zhèn (朕) were generally imported loanwords, it nevertheless led to a polite avoidance of pronouns throughout East Asia. This still persists, except in China, following the May Fourth Movement and the Communist Party victory in the Chinese Civil War. In Modern Standard Mandarin, the first-person singular is wǒ (我), which gradually emerged from a common epithet expressing “this [worthless] body.”

_{from Wikipedia ― Royal “we”}

짐이 백성의 뜻을 좇아 황제 위에 오르고자 천지에 고하노라.

_{from “대한 제국 (Korean Empire)” written by Joohyun Yoo (柳周鉉).}

짐 means "I" used by a king. Even when we translate a line spoken by a king in English movies, we use 짐 for "I".

From what I've heard, 짐 was reserved for the emperor, which meant the Emperor of China during most of the Joseon dynasty (except for the brief period of the Korean Empire (대한제국)). So, during these days, kings of Korea commonly used 과인.

According to Namu wiki:

하지만 [과인은] 스스로를 낮춰 부르는 말인만큼 한국 사극에 나오는 것처럼 무분별하게 조선의 국왕들이 과인(대한제국 이후로는 짐)이라는 말을 일상적으로 자주 쓰는 것은 아니었다. 주로 자책을 하거나 겸양할 때 등 스스로를 낮춰야 하는 상황에서 주로 쓰고, 평소에는 '나' 를, 정확히는 나 여(余) 자를 썼다. 다만 余는 '나'라는 뜻을 가진 한자식 표현이기 때문에 실제로는 나라고 말하고 기록할 때 여라고 했는지 혹은 말 할 때도 여라고 했는지는 알기 어렵다.

In any case, there are no more Korean-speaking monarchs, so these words are almost exclusively used in historical dramas, which aren't that historically accurate anyway. (For one thing, ancient Korean kings obviously did not use modern Korean!)

• Namu wiki is usually even less trustworthy than Wikipedia, so take the above quote with a grain of salt. (Sorry, I couldn't find a better source.)