The matter is now extremely urgent - we can't put it off any longer.
Tips
usage
Rarely stands alone. Almost always paired: 睫毛 (eyelashes), 假睫毛 (false eyelashes), or in idioms like 迫在眉睫 'pressing on the eyebrows and lashes' = imminently urgent, 目不交睫 'eyes never meet at the lashes' = unable to sleep a wink.
memory
Radical 目 (eye) on the left tells you it's about the eye. The right side 疌 gives the sound (jié). Lashes are tiny on the eye - picture a row of fine hairs along the lid.
Left eye radical - the indexing element, originally a pictograph of an eyeball with its inner detail visible. Anchors 睫 in the eye-anatomy family with 眼 (eye), 瞳 (pupil), 眉 (eyebrow), 眶 (eye-socket). The radical states plainly: this character names something that grows on or around the eye.
phonetic
疌jié
quick; nimble (here phonetic)
Right 疌 supplies the sound jié with no drift, and adds a faint flavour of quickness: 疌 is the original form behind 捷 (swift) - so 睫 carries the picture of fast-blinking lashes. Same phonetic series gathers nimble-and-flicker meanings, fitting for the flutter of eyelashes.