Could you give more details about where you heard this expression? It is probably some kind of bill, but the meaning may depend on where the speaker is from, and possibly whether the context is modern or in the past. My understanding of 'tab' is a (usually informal) account of how much you owe someone. For example, a poor family who is unable to pay for their food from time to time might have a 'tab' at the local grocer's store. The shopkeeper will supply them with goods that they need and add the price to their 'grocery tab'. When they get some money, perhaps when they're paid at the end of the month, they'll pay their tab (settle their account).

I have never heard anyone refer to a grocery tab. It sounds like something that might have existed in small towns in the past. “Tab” is usually used in bars. A bar might offer customers a choice of paying for each round of drinks as it is served, or to “run a tab” which would be settled when the customers are about to leave (“paying the tab”). “Tab” could also be used in similar situations where payment is collected at the completion of a project, though it’s rather informal for something like professional fees. I’ve never heard of this practice (or “tab”) in retail. But that’s not to say that it doesn’t or didn’t exist.

"tab" is American English, to mean the bill - the piece of paper that has the total amount owing.