There are a number of occasions where the first person to claim ownership or interest in something actually gets it. Such is the case with the term first dibs, or in some cases simply dibs. Calling dibs generally leads to the same conclusion — one person has acquired the right of first refusal. A person with first dibs may choose the most desirable of several options, or even elect to pass on the situation altogether. What matters most in this situation is the exclusive ability to accept or deny ownership rights without competition.
The origin of this phrase is somewhat murky. Some sources suggest that an ancient children's game similar to jacks used special counters called dibstones. These dibstones would be divided amongst players according to the rules of the game, with some receiving more dibstones than others. It is possible that schoolchildren may have informally shortened the name "dibstones" to a more manageable "dibs." The phrase "first dibs" appeared fully formed in American literature around the turn of the 20th century. British children were said to use the term "bags" interchangeably with "dibs" during the late 19th century.
Another theory on its origins concerns a slang word for money. It is believed that the word dibs was used informally in the 1800s to describe a basic currency, such as a dollar or pound. Although this use of the word dibs is now considered archaic, it would not have been unusual for an 19th century citizen to hope for a million dibs in the bank. Perhaps the idea of first dibs arose from the first cut of a large financial inheritance or gift.
One of the most logical theories surrounding this term suggests a corruption of the word "division." It doesn't appear to be much of a leap from "div" to "dib," and the idea of first dibs does imply a possible division of the wealth. A similar sounding phrase, "divvying up the loot," also suggest that's "divvying" and "dibbying" are not that far apart in root meaning. Unfortunately, there are not many sources which support a connection between "division" and "first dibs."