Being a grandma is no excuse for falling behind culturally.
I don't mean you have to be aware of every celebrity twitch. What I mean is it's not good to use your own advancing age to ignore what's happening in our culture. And in our culture, technology is a big deal.
Even if you don't use technology, it's a good idea to know something about it. Otherwise, sooner or later you'll find yourself speaking a different language from your grandchildren.
Traditionally grandparents hang on to technology that was cutting edge when they were younger, and shy away from what is newest. That isn't true of all grandparents, of course; some of us can't wait to show off how cool we are -- we Twitter, and we don't care who knows it!
Part of understanding and using technology is awareness of its risks and dangers. The NetSmartz website has easy-to-understand explanations of those risks and dangers, with special sections for parents and guardians, as well as for children of every age.
I encourage you to check it out, educate yourself, then share what you've learned with the grandkids you love.