The main use of "se" here is to describe that the grandfather fell without prior knowledge that he was going to fall. Yes, I know that sounds weird, especially in this context, but it's why you would use caerse instead of caer.
Mi abuelo se cayó. ≠ Mi abuelo cayó. That's for this context; if you were to say "Mi abuelo cayó," people would understand.
This has to do with "caer" being literally translated as "to fall" (as in, something is falling from the sky). There is no verb that means "to fall down," so Spanish speakers either use "dejar caer," which means "to let fall," or "caerse," which means "to fall oneself," (I understand that makes no sense in English, but that's the literal translation). So, when you use caerse, it means the grandfather fell himself, or fell down.
Hope this helps!
I am glad someone pointed this out. Here are some links to back the statement up.
It seems for this verb the reflexive pronouns are generally used for people or accidents. However, sometimes they are not depending on what emphasis is desired.