Several parts combine into one character.

紀 is a phonetic-semantic compound: 糸 (silk thread) + 己 (jǐ, "self" — providing the sound). The original meaning was concrete: the leading thread / main strand of a woven fabric — what one organizes the rest of the threads around. From this textile origin grew an extraordinary semantic chain: leading thread → guiding principle / standard → record / chronicle → era / generation. The character documents how the East Asian conception of "era" developed from the practical metaphor of "the thread that organizes the cloth."

Korean reading "gi." 世紀 (segi, century — used universally for "21st century" etc.), 紀元 (giwon, era / epoch — used in giwon-jeon "BC" and giwon-hu "AD"), 紀錄 (girok, record — though modern Korean increasingly writes this with 記錄), 紀念 (ginyeom, commemoration — though 記念 is now standard), 風紀 (punggi, public morals / social discipline — punggi-mullan denotes "moral degeneracy"). The "record" sense in Korean has largely shifted to 記 (also gi), with 紀 reserved for "era / chronicle."

Mandarin jì, 4th tone (simplified 纪). 世纪 (shìjì, century — universal modern time vocabulary), 纪录 (jìlù, record), 纪念 (jìniàn, commemoration), and the politely formal 年纪 (niánjì, "year-thread" = age — used as a polite alternative to 岁数 suìshù: 你多大年纪? "How old are you?" is more deferential than the casual 你几岁?). 纪律 (jìlǜ, "thread-rule" = discipline — central to Chinese institutional vocabulary, especially Communist Party 党纪 dǎngjì "party discipline").

Japanese on-reading キ (ki) — 世紀 (seiki, century), 紀元 (kigen, era / epoch — 紀元前 kigen-zen "BC"), 紀行 (kikō, "travel chronicle" = travelogue — a recognized Japanese literary genre, with classics like Bashō's 奥の細道 Oku no Hosomichi being a 紀行文学 travel literature). The 21st century 二十一世紀 (nijūichi seiki) is everyday Japanese vocabulary.

Memory aid: silk thread (糸) and self (己) — the leading thread that organizes everything else became "era" and "record."