Several parts combine into one character.

甘 is an indicator character (指事字): take 口 (mouth) and add a single horizontal stroke inside it. That extra mark depicts something held in the mouth — and what one holds and savors is what tastes sweet. The character's elegance is in its abstraction: rather than depicting any specific sweet object, it depicts the act of holding a flavor on the tongue. 甘 anchors a small but flavorful family: 甚 (extreme — extension from "very sweet" to "very much"), 甜 (modern Mandarin term for "sweet" with mouth radical added).

Korean reading "gam." 甘味 (gammi, sweetness — used in both food and aesthetic contexts: "sweet voice"), 甘酒 (gamju, sweet rice drink — Korean version of amazake), 甘草 (gamcho, licorice — used in herbal medicine; the idiom "licorice in the medicine cabinet" describes someone who appears in every group, ubiquitous), 甘苦 (gamgo, "sweetness and bitterness" = ups and downs of life), 甘酸苦辛 (gamsangosin, "sweet-sour-bitter-spicy" = the four classical tastes of Asian cuisine — Western cuisine's "sweet-salty-sour-bitter" differs by including salty and excluding spicy).

Mandarin gān, 1st tone. 甘 (gān, sweet — formal/literary; everyday Mandarin uses 甜 tián), 甘苦 (gānkǔ, sweet and bitter), 甘心 (gānxīn, "willingly / contentedly" — 心甘情愿 xīngān qíngyuàn "willing and content"), 甘肃 (Gānsù, Gansu Province — northwest China). 甘 leans formal/poetic in modern Mandarin; the everyday spoken word for "sweet" is 甜.

Japanese on-reading カン (kan) — 甘味 (kanmi, sweetness — in food contexts like 甘味料 sweetener), 甘草 (kanzō, licorice). Kun-reading あまい (amai, "sweet") — 甘い (amai). Beautifully, Japanese extended the metaphor: 甘い literally means sweet to the taste, but figuratively means "lenient / naïve / too easy / soft." 考えが甘い (kangae ga amai, "thinking is sweet") = "your thinking is naïve / underestimating the difficulty"; 採点が甘い (saiten ga amai, "grading is sweet") = "lenient grading." A second kun-reading: 甘える (amaeru, "to act spoiled / depend on someone's indulgence") — a culturally specific Japanese concept of acceptable dependency, where someone (especially a child or close family member) deliberately invokes another's tolerance. 甘え (amae) is one of the most frequently cited "untranslatable" Japanese psychological terms.

Memory aid: a mouth (口) holding something inside (the extra stroke) — what is held and savored is the sweet taste.