As a verb, broach means to bring up or introduce a sensitive issue. As a noun, a broach is one of those dowdy pins your Great Aunt Edna wears. Telling her not to wear it is a subject you should probably not broach.
Let's say you want to go on vacation with a friend and you ask your dad because he is more likely to say yes. He will probably tell you that he will broach the subject with your mom and let you know. In a less common (and older) usage of broach, if you put a hole in something in order to get out what's inside you broach it. The piercing tool you use is also called a broach. Think of piercing someone with your idea the next time you broach a touchy issue.