The Baudelaire Fortune is a large, unspecified amount of money that was left behind by the Baudelaire parents to the Baudelaire children.
However, due to their parents' very specific will, they are not allowed to use a single cent until at least one of the orphans turns 18 years old; in this case, Violet Baudelaire would allow to use it the soonest as she is 14 years old in the beginning of the series. Because of the will, Arthur Poe at Mulctuary Money Management refuses to allow to orphans to access it. The fortune is also not to be used for any of the Baudelaire guardians.
The fortune is Count Olaf's main incentive for tormenting the Baudelaires in the first place, but it has been debated that the primary reason for his involvement in the Baudelaires' lives could be something else, such as his relationship with the Baudelaire parents.
It is ironic that the Baudelaire fortune was intended to better the children's lives, when it actually became a burden for them due to Count Olaf's pursue of the orphans. If the Baudelaires were never to inherit the fortune, then Count Olaf may have left them alone and they would never have experienced a series of unfortunate events. The Baudelaires also occasionally live in borderline poverty, as they can't afford a basic bed in The Bad Beginning, and are at the mercy of the world in The Hostile Hospital and onwords, although it could be argued they were at the mercy of the world before then.
In The Penultimate Peril, it appears that Mrs. Bass (a teacher from Prufrock Preparatory) robbed Mulctuary Money Management (rumor claims that she stole the Baudelaire Fortune). In Mrs. Bass' hotel room, Sunny sees a pile of large bulky bags with PROPERTY OF MULCTUARY MONEY MANAGEMENT stamped on them. The Austere Academy mentions Mrs. Bass was arrested for bank robbery.