expression, godan verb (-ku)
enlighten; open someone's eyes
Literary idiomatic expression meaning to dispel ignorance or open someone's mind to knowledge. Often used in formal or didactic contexts.
彼の講演は多くの若者の蒙を啓いた。
His lecture enlightened many young people.
啓蒙 is a noun meaning 'enlightenment' or 'education', while 蒙を啓く is a verb phrase meaning 'to enlighten'.
From the kanji 蒙 (ignorance) and 啓く (to open, to enlighten). The phrase literally means 'to open ignorance'.