To murder is to kill, and it's illegal. Murder is one of the worst crimes of all.
While murdering sometimes means mangling something (like murdering a speech you were trying to give) it usually means killing — but not just any killing. If you kill someone by accident or in self-defense, that's not murder. If a soldier kills an enemy, that's not murder. Murder is a planned, illegal form of taking someone's life. If you read a law book, you'll see how complicated murder can be.