If you insult someone, you have offended that person — either intentionally or unintentionally — through your actions or words. You might insult your host if you refuse to try the dessert he made from pasta, nuts, and chocolate sauce.
As a noun, an insult means rude words or actions. If you tell the umpire he needs glasses, then you've made a verbal insult. If, after the umpire calls your team out, you make an obscene gesture in his general direction, you've made another kind of insult. Either insult can potentially get you thrown out of the game.