When you insert something or someone, you put it into something else. You could insert yourself into a conversation, or you could insert a comma into the sentence you just wrote.
The verb insert comes from the Latin in-, meaning “into,” and serere, meaning "to join." When you insert yourself into a conversation, you’re joining in, whether your friends want you to or not. Insert can also mean to fit snugly into, or to tuck. You might fit a card into an envelope that fits it perfectly, or insert first one leg and then another into a pair of tights.