I'd appreciate any insights regarding the following quote:

from THE NATURE OF SPACE AND TIME , year 2000, a series of "competing" lectures by Hawking and Penrose...not a book for the casual reader. While there is a lot of the implied conceptual mathematics I don't understand, the following statements by Penrose were intriguing (page 32)

I understand that with a time-like interval enough time passes for there to be a cause-effect relationship between two events; not so with a space-like interval. I think what I am asking is "how do the different solutions of GR equations lead to conclusions about the types of singularities." Any ideas about what is a space-like vs timelike infinity?
Thanks