The quote is saying that love leaves an impact on you. The author poses a counterpoint to the common sayings "love is gentle, love is kind" by comparing it to an animal or a monster that causes indelible marks.
It is also talking about the sympathetic words that you may hear when you're injured by love. As soon as you get over it, the words will stop coming from people, and it won't hurt as much (but you'll still remember it: "the wounds never close".)
