Several parts combine into one character.

綿 is a compound ideograph: 糸 (silk thread / textile fiber) + 帛 (white silk fabric). The original picture was "fibers continuously joined to form fabric" — by extension, the cotton-like puff of fibers that have been spun into thread. From this concrete textile origin grew a beautiful metaphorical extension: "fibers unbroken / continuous" became "continuing without interruption" = 綿綿 (continuously, in unbroken succession).

Mainland China made an interesting taxonomic split: for the cotton plant itself, mainland uses 棉 (with the wood radical 木 instead of silk 糸), reserving 绵 (the simplified form of 綿) for "continuous / soft." Korea and Japan kept both meanings under the single character 綿.

Korean reading "myeon." 綿絲 (myeonsa, cotton thread), 純綿 (sunmyeon, "pure cotton" = 100% cotton — clothing label vocabulary), 綿布 (myeonpo, cotton fabric), 綿綿 (myeonmyeon, continuous / unbroken — used poetically: "the unbroken tradition"), 脫脂綿 (talji-myeon, "fat-stripped cotton" = absorbent cotton / surgical cotton).

Mandarin mián, 2nd tone — split into two characters in simplified script. 棉 (mián) = cotton plant: 棉花 (miánhua, "cotton flower" = the cotton plant / cotton fiber), 棉衣 (miányī, cotton-padded clothing — winter staple in northern China), 棉被 (miánbèi, cotton-padded quilt). 绵 (mián) = continuous / soft: 绵延 (miányán, stretching continuously), 连绵 (liánmián, continuously connected — used for mountain ranges, days of rain, etc.). The split is functional: physical cotton vs metaphorical continuity.

Japanese on-reading メン (men) — 綿花 (menka, cotton plant), 純綿 (junmen, pure cotton), 綿密 (menmitsu, "fiber-dense" = meticulous / detailed — beautiful metaphor: thoroughness as densely packed fibers). Kun-reading わた (wata) — 綿 (wata, cotton wool — the puffy fiber form, before being spun), 真綿 (mawata, "true cotton" = silk floss, the fluffy silk product extracted from broken cocoons; an unusual case where わた means silk floss rather than cotton). Japanese also uses 綿 in idioms of softness and meticulous attention.

Memory aid: silk threads (糸) plus white silk fabric (帛) — fibers continuously joined. The same imagery generated both the noun "cotton" and the adjective "unbroken."