To bring up a topic for discussion, usually one that is difficult or sensitive.
From Old French 'brochier' (to pierce), from Latin 'brocchus' (projecting). The meaning shifted from 'to pierce' to 'to open up a container' to 'to open up a topic of discussion' by the 1500s.
A broach started as a sharp tool that literally pierced things, but speakers realized that bringing up a difficult topic was like 'piercing through' awkward silence—so the word evolved its modern meaning through metaphor!
Complete word intelligence in one call. Free tier — 50 lookups/day.