I'm going to keep my answer relatively simple because I think it should be. I think there are several levels on which this can be interpreted.
Kylo Ren is "killed" and is replaced by Ben Solo. Hence the Skywalker side of him rises and he helps defeat the Emperor. This is all metaphorical of course, but on a certain level, it isn't. There are several references to Episode VIII when Rey almost takes Kylo Ren's hand to join him. She later clarifies that it was Ben's hand, not Kylo Ren's hand that she wanted to take. Hence Ben Solo represents the "Skywalker" side of the character.
After Rey defeats Palpatine, she dies, but is brought back by the life force transfer of Ben Solo. She then either literally or metaphorically (however you interpret it) becomes, or at least identifies as, a Skywalker, as evidenced by the ending of the film where she is asked what her family name is and she replies "Skywalker".
It is symbolic of the force winning over the dark side
The Skywalker family has become symbolically synonymous with The Force while the name Palpatine has become synonymous with The Dark Side. So when Rey claims to be a Skywalker, it puts to rest her own questioning of her identity and destiny. Skywalker has risen and defeated Palpatine within herself.