"Keeping pace" with something means moving quickly enough so that you don't get left behind.

You can use this phrase to talk about someone's actual speed:

I couldn't keep pace with the rest of them, so I told 'em to go on ahead without me.

Or you can talk about "keeping pace" with how quickly things change, like:

Technology changes so quickly; it's pretty much impossible to keep pace with it all.

They have some old-fashioned ways of thinking. I guess that you could say that they haven't kept pace with a lot of the societal changes that have been going on over the last few decades.