Hot Rod, whose importance to the film has been increasing gradually through the course of the movie (especially since the fall of Ultra Magnus on the Planet of Junk), engages in the Epic Battle with Galvatron. Viewers are intended to recall the Epic Battle between Optimus Prime and Megatron, in which Hot Rod briefly attempted to intercede to thwart treachery, thus distracting Optimus and through the Best of Intentions causing the rest of the movie. Here Hot Rod redeems himself by (naturally enough) defeating Galvatron. To do same he opens the Creation Matrix, which various other characters (Ultra Magnus and Galvatron) had attempted to do earlier. In some appearances of the Matrix in the comic series the red pip visible on the Matrix in this film is a button you press to get it open -- most characters are renedred helpless to Unleash the Power of the Matrix because it doesn't occur to them to push the button. Hot Rod doesn't press the button either, but it opens anyway.
Hot Rod becomes Rodimus Prime by way of opening the Matrix (and because a reverbed Optimus Prime voiceover comes in right then to say "Arise, Rodimus Prime"). The overt symptoms of this change are his growing a third taller and his sportscar version becoming a sportscar-like panel truck. The bit about Optimus' voice coming in with the "arise" statement was a nice touch, but I have to wonder if it was an attempt on Hasbro's part to transfer the affections of scads of ten year-olds from Optimus to Rodiums. It's not clear whether it worked, but by eliminating Optimus, as discussed earlier, they wiped out the single most appealing character in the series, and made little effort to regain it with Rodimus (the "younger, hipper Prime") or any other character. The toy version of Rodimus Prime turned out to be a cheap plastic knockoff of much lower manufacturing quality than the toy version of Optimus.
Presumably to ensure the continuation of the series, Rodimus throws Galvatron through Unicron's side and out into space. That usually has a fatal effect on minor characters, but since Galvatron was the newly introduced character for which Hasbro presumably had high merchandising hopes, they likely didn't want him killed off. Galvatron doesn't appear for the rest of the film, but he did start appearing regularly in the TV series up until its cancellation.
This is the only real inication that Jazz, Bumblebee or Cliffjumper (all of whom had been on the moon bases eaten by Unicron) survived the ordeal -- they briefly drive past after Hot Rod/Rodimus defeats Galvatron.
Autobot Creation Matrices can be harmful to the health of Planet-sized robots. Here we see the dramatic "death" of Unicron, with more of the blue rays of light motif. Unicron's head pops off and goes into orbit around Cybertron, leaving room for a sequel (which never came), and reimbursing Cybertron for one of its two destroyed satellites.
Not shown here is the brief celebration scene on Cybertron where Rodimus Prime says some enthusiastic and authoritative leader-stuff about the end of the Cybertronian Wars. This idea lasts approximately as long as the next TV episode, at which point the Cybertronian Wars have kicked right back up again. For the sake of continuity the Decepticons resume the TV series in a weakened position, but still think up a Dastardly Scheme every episode. In the leaderly speech Rodimus reiterates the expression "Till All Are One," initially uttered in Optimus' dying breath and here repeated earnestly by all the Autobots, but it doesn't come up again. Unity isn't a profitable thing for a toy company.
I've pasted together the character credits here. Some noteworthy entries are Peter Cullen as Optimus Prime, Monty Python's Eric Idle as Wreck-Gar (the chief of the Junkions), Judd Nelson as Rodiums Prime/Hot Rod, Leonard Nimoy as Galvatron, Casey Kasem (snipped out of the credit frames, sorry) and Orson Welles as Unicron.retreat, flee