Tom, the oldest of the Bertram children, stands to inherit his father's estate. He starts off the novel as Mary Crawford's love interest, and he's instrumental in getting the "Mansfield theatricals" off the ground. Tom is also responsible for a lot of the major plot points that dominate the start of the novel. His gambling debts are part of the reason why Sir Thomas has to go to Antigua to take care of his financial problems. Tom's debts also mean that Edmund won't be able to move into the Parsonage at Mansfield Park when he's ordained, which of course results in the Grants and the Crawfords moving in. And Tom introduces Mr. Yates, Julia's future husband, to the Bertrams.
But after doing all of this, Tom disappears for hundreds of pages, only to turn up near the end of the book dying from a serious illness. However, Tom's disappearance and subsequent illness are definitely important, too. Tom going away for such lengthy periods allows Edmund to step into the role of eldest son. This is important because it gives Mary an impression of Edmund that isn't entire accurate, and fuels her fantasies of Edmund somehow becoming the eldest Bertram, or at least independently wealthy, someday, which she tactlessly expresses after Tom falls ill (45.13). Tom's absences also let Edmund assume the role of dominant, and favorite, son in the family.
And after Tom recovers from his illness he is hugely changed, and much more respectable: "He became what he ought to be, useful to his father, steady and quiet, and not living merely for himself" (48.4).
Even though Tom disappears a lot and seems to turn into a "good" son by the end of the novel, he's actually really important in moving the plot along and in causing things to happen. Tom's illness especially has a lot of symbolic meaning – it's no mistake that Tom only reforms his ways after he's had a near-death experience, after all.