The phrase is usually used by children to mean, “I claim ownership of that.” However, World Wide Words, a site I frequently use, tells me there is no definitive explanation of the origin. There are dozens of children’s games that have had “dib” or a similar expression in their name. H.G. Wells used “dibs” as slang for money. Perhaps the most logical explanation is that “dib” is an abbreviation of “division” or divide.” But that logic isn’t backed up by evidence.