To nullify something means to make it invalid or ineffective. A peace treaty is an attempt to nullify aggression and division within a region.
If you take a null, or a zero, and make it into an action you can take, and you’ve got nullify — the act of making something void or zero-like. If you have an argument with your friend, it might nullify the fun you had together that day. This word is particularly used in legal language — a divorce nullifies a marriage — or in business disputes where you are trying to nullify someone else’s actions or plans.