In the YouTube video A Man Drank 3 Liters Rum Everyday Since Age 13. This is What Happened To His Liver it is mentioned that "No more than 1 to 2 shots per day, without rollover, of hard liquor [...] is the recommendation." What is rollover?
A rollover is when an unused portion of something in one period is carried on into the next period.
In the context of the example, it means that each day, someone is allowed to drink 1-2 shots. If they don't drink 1-2 shots on a particular day, it doesn't mean that they are then allowed to carry that allowance to the next day, and drink 4 shots safely (or 14 shots on a Saturday night, and then no drinks at all for the rest of the week).
Just to add on to PeteCon's correct answer: This use of "rollover" is fairly recent, which is probably why it does not appear in many standard dictionaries.
The "original" use, starting from the 1940s was with financial transactions, and meant to take the funds from one transaction and "roll them over" into a new transaction. I've most often seen this used with retirement plans, which you can "rollover" from one bank or investment house into another of a similar type.
More recently, cell phone companies started using this as a marketing incentive, allowing customers to "rollover" their unused cell phone minutes to the next billing period. So for example if you were allowed 3000 minutes per month, but you only used 2500, the next month you would have 3500. Although most companies now offer unlimited calls and texts, many still do this with cell phone data plans.
The passage reflects this latest use. You get 1-2 drinks per day, but you can't save them for a later day if you don't actually drink them.