The ending reveals that Andrea Beaumont is the Phantasm, and that she killed the mobsters to avenge her father. In my opinion, that reveal is why the film is remembered: the mystery looks like a hunt for a stranger, and it turns out to be the story of the one person Bruce Wayne let in.
The finale at the World of the Future fair puts the three threads together. Andrea faces the Joker, the man Valestra hired to kill Batman, who instead killed Valestra. She and the Joker vanish as the fair blows up, while Bruce survives and is left with her locket and the photo inside. Andrea then leaves Gotham by ship. It could be argued that the locket matters more than the explosion, because it is the only object that survives from the life Bruce nearly chose.
Why does the reveal land? Because the film plants it early. In the flashbacks, Bruce proposes, and Andrea ends the engagement by letter after her father Carl runs into trouble with the mob. Carl is tied to the first two dead men and to Valestra, so the victims are not random. Arthur Reeves, who betrayed the Beaumonts, is poisoned by the Joker and confesses, and the list of people with a reason to hate the old Gotham mob points straight at her. Stacy Keach voicing both the Phantasm and Carl Beaumont is, perhaps, the neatest clue of all, since the killer and the father the killer avenges share one voice.
The Joker's role is worth separating out. Mark Hamill's Joker is not the mastermind but a hired killer who turns on the man who hired him, and Andrea's confrontation with him is what pushes the story to its end. Compare that with Batman (1989), where Jack Nicholson's Joker is the central villain whose origin drives the plot, or with Batman Returns, where Selina Kyle is pushed to her apparent death and comes back as Catwoman. Those films treat the person who is wronged as a rival who is mostly beyond saving. Here, the wronged person is someone Bruce loved, which is a different kind of loss.
The parallel with Batman Begins is also worth drawing. There, Bruce's parents are shot outside an opera house, and the grief becomes the engine of his crusade. In this film, Bruce commits fully to becoming Batman after Andrea's letter, so a second loss reinforces the first. The result is a hero shaped by two losses rather than one.
The last beat sends Batman back to guarding the city alone. That choice sets him up as the lonely figure of the animated series, which is the most direct answer to how this film connects to Batman: The Animated Series. The film also reached US theaters in 1,506 locations on Christmas Day 1993, and its small gross suggests that audiences found it later, on home video and streaming, rather than at the multiplex.