The traditional account* holds that the form of ㄹ l is the outline of the tongue, 舌[…]之形, but does not specify what this means. Gari Ledyard proposes that it was a graphic simplification of Phagspal, ultimately from Tibetan ལ l, though the iconic considerations of the traditional account may have determined the form that this simplification took.
* Hunmin Jeongeum Haerye “Explanations and Examples of the Proper Sounds for the Instruction of the People” (1446), defining and explaining the script now known as 한글(han-geul, “Great script, Korean script”) in South Korea and 조선글(joseon-geul, “Korean script”) in North Korea.
From Middle Koreanㅭ(-lq), from Old Korean尸(*-l). The Old Korean form (up to the thirteenth century) was primarily an irrealis verbal nominalizer, rather than an adnominal suffix as it is now. In fifteenth-century Middle Korean both the nominalizing and adnominal functions were in use, but the nominalizing function was already quite archaic. Since the sixteenth century, the suffix has only had an adnominal meaning.
After consonants, the allomorph -을 (eul, “-eul”) is used.
-ㄹ (-l) is appended to the sequential form. Similar to a future participle, the resulting determiner indicates that the referent of the following substantive will perform the action described by the verb to which -ㄹ (-l) is attached:
가다 (gada, “to go”): 가니 (gani, “ga-”) + ㄹ (l): 갈 (gal, “who will go; that sb will go to/at/by...”)
묻다 (mutda, “to inquire”): 물으니 (mureuni, “mureu-”) + ㄹ (l): 물을 (mureul, “who will inquire; that sb will inquire”)
날다 (nalda, “to fly”): 나니/날면 (nani/nalmyeon, “na-/nal-”) + ㄹ (l): 날 (nal, “that will fly”)
The suffix -ㄹ (-l) is frequently used along with several dependent nouns, such as 것 (geot, “thing”) and 때 (ttae, “time”), for grammatical purposes. As an irrealis mood marker rather than a tense marker, it can either denote the future tense, or nothing:
(future, intention) 그 친구는 이번기회에 고향집을 찾을것이라고 했다. (Geu chin-guneun ibeon gihoee gohyangjibeul chajeul geosirago haetda., “He said he will visit his hometown by this chance.”)
(future, guess) 물이 차가울것같다. (Muri chagaul geot gatda., “I guess the water is cold.”)
cf. 물이 차가운 것 같다. (Muri chagaun geot gatda., “The water seems cold.”) / 물이 차가웠을것같다. (Muri chagawosseul geot gatda., “I guess the water was cold.”)
물이 차가울 것 같았다. (Muri chagaul geot gatatda., “I guessed the water was cold.”) / 물이 차가웠을 것 같았다. (Muri chagawosseul geot gatatda., “I guessed the water had been cold.”)
(no tense) 그가 하는말중에 믿을만한 것이 있을리가 없다. (Geuga haneun mal jung-e mideul manhan geosi isseul riga eopda., “Among the words he says, what is worth believing cannot ever exist.”)
(no tense) 목발은 발이나 다리를 다쳐잘걸을수 없을때사용한다. (Mokbareun barina darireul dachyeo jal georeul su eopseul ttae sayonghanda., “We use crutches when we don't walk well due to foot or leg injuries.”)