All right, all you legal beagles, if I butcher the exact definition, come at me. A bonded winery is a winery that has taken out an insurance policy that will cover their excise tax liability due to the feds. Yep, it all has to do with taxes.
When a winery establishes itself with the TTB (Alcohol and Tobacco Tax and Trade Bureau), it also has to calculate its bond coverage. The winery does this by estimating the total amount, in gallons, of wine that they may have stored on their property at any given month of the year, while also taking into account the alcohol content of said wine. This calculation then determines the amount of bond coverage the TTB requires them to take out in order to cover their tax liability.
But! Not all wineries require a bond. In 2015, the Obama Administration signed the Consolidated Appropriations Act, which allows smaller wineries — those that produce a small amount of wine and therefore have a much lower tax liability — to be exempt from having to hold a bond. If you are really interested in whether or not you need a bond for your winery, I am not a lawyer, so you should probably talk to one.