I think it is something we just encounter everywhere in life, right in front of our eyes. Everything comes and goes, people we love are born and die. Buddhism extends the idea to everything in the universe, even perhaps the universe itself. Spring, summer, fall and winter, time passes.
The only particularly "Buddhist" part of it is our approach to the impermanence that is naturally all around. We do not cling, develop non-attachment, embrace the change. We do not clutch at sand castles, in desperation trying to keep the tide from washing them away. We flow with the tide.
This embracing attitude comes mostly on the cushion through our Zazen, but we learn to carry it off the cushion throughout our lives ...more than just an intellectual idea, it becomes the actual way we approach life. I think. (Another Buddhist idea is that each moment is complete and just what it is, so time does not pass ... but that is just another tool on our toolbelt, also learned on the Zafu)
All things are impermanent. Time passes and does not pass. No birth, no death.
I think impermanence also addresses our innate resistance to change. I am coming up on a pretty big change in my job and even though I tend to like change, I always feel a little anxious letting go of my usual routine.