When you have dibs on something, you've made a claim to it — you have a right to own, control, or share it. You and your brother might have grown up arguing over who had dibs on riding in the front seat of the car.
You'll often find the word dibs in the phrase "have first dibs on." For example, you could say, "I wanted the chocolate donut, but my sister had first dibs on it." Usually, having dibs on something is merely a matter of being the first person to claim it out loud. It's a late 17th century American English word that comes from children's slang, a shortened form of dibstone,"a jack in a children's game."