The signature compound is 耄耋 ('octogenarian / very old'). Classical glosses set 耄 around 80-90 and 耋 around 70-80, so the four-syllable expression 耄耋之年 is the polite way to say 'very advanced age'. Spoken Chinese still prefers 高龄 or 上了年纪.
register
Literary register, but still alive in newspapers and birthday couplets. Don't confuse with 耆 (60s-70s) — Chinese tradition slices old age into named decades, and the pairing 耆耋 covers the whole upper range while 耄耋 sits at the top.
Bottom 毛 (hair) supplies the sound (máo → mào, tone change), and a secondary semantic hint: the white 毛 (hair) of advanced age. So an elder (耂) whose hair (毛) has gone white — extreme old age.
