Syllable division derived from spelling — this word is not in the pronouncing dictionary, so no phonetic transcription is shown rather than a guessed one.
button-down is an adjective meaning "unimaginatively conventional". It carries 2 recorded senses.
unimaginatively conventional
“a colorful character in the buttoned-down, dull-grey world of business”
of a shirt; having the ends of the collar fastened down by buttons
“Brooks Brothers button-down shirts”
Definitions, synonyms and semantic relations for button-down come from Princeton University’s WordNet. Commonness is measured against a corpus of everyday English. Full sources and licences.