If you're looking for an answer to why the sugar bowl is so important, or what's inside it, there's some bad news: the books never reveal answer those questions. By the end of the series, many questions have been answered, but there are also some mysteries that remain - and the sugar bowl is the biggest one.
We know that the sugar bowl was taken from Esmé Squalor's tea set, and that she is determined to get it back at all costs. Esmé says that Beatrice stole it from her, but Lemony Snicket also says that he stole the sugar bowl, so it's uncertain whether Esmé is incorrect or whether Lemony and Beatrice were complicit in its theft. While there's no official word on what the sugar bowl contains, there are some solid fan theories.
In the eleventh book of the series, The Grim Grotto, the Baudelaires go on a search for the sugar bowl that brings them to the Gorgonian Grotto - a hidden underwater cave where many different objects wash up. Due to the tides, things can wash up into the grotto, but they cannot escape, which allows it to act as the perfect quarantine for an extremely dangerous species of fungus called the Medusoid Mycelium. This mushroom spreads extremely quickly, and is so deadly that a single spore can kill a person within an hour in the most horrible way - by growing mushrooms inside their mouth, throat and lungs until they choke to death. If someone were to get their hands on a sample of it, the Medusoid Mycelium could effectively be used as a biological weapon.
One fan theory, therefore, is that the sugar bowl contains an antidote to the effects of the Medusoid Mycelium. It's possible to cure someone of the mushroom's effects using common horseradish or wasabi (if you look closely at V.F.D.'s underground tunnels in season 2, you'll see a sign pointing in the direction of the Horseradish Factory), which dilutes the fungus. Another extremely effective cure is the fruit of a special hybrid tree, created by cross-breeding horseradish and apples. Some believe that the Sugar Bowl contains fruit from this tree, or seeds from the apples, so that new trees could be planted.
Another fan theory is that the sugar bowl contains evidence that could exonerate Lemony Snicket, who is on the lam because people believe he is guilty of the arsons committed by Count Olaf. The possibility of the sugar bowl containing some kind of information would certainly fit, given how much members of V.F.D. value information. Yet another theory is that the sugar bowl is dangerous, and contains some kind of weapon - perhaps even a sealed sample of the Medusoid Mycelium.
Speaking in an interview with The Observer last year, A Series of Unfortunate Events author Daniel Handler said that about one fan every year writes to him, having solved the mystery of the sugar bowl. "The whole answer of the Sugar Bowl is solvable," Handler said, though naturally he didn't give away the solution. Perhaps season 3 will offer some fresh clues about what exactly is so important about the Vessel For Disaccharides, so that readers of the books can finally find a clear answer.
A Series of Unfortunate Events season 2 is now available on Netflix.