I know my first impression is it refers to 'times'. Then you explained it refers to 'characteristics of our grandparents' age'. I don't know somehow when I read the sentence again and again I thought it might refer to 'lives'. That's why I asked you. Now since you confirmed I think I am wrong.
The sentence should go like this:
If there is one main characteristic of the modern world that makes our lives different from the characteristics of the ages when our grandparents lived, it is probably speed. Is that right?
Looking forward to hearing from you.
Thank you in advance.