Here is the shortest way I can describe the difference between old-school (Newtonian) spacetime and modern, relativistic (Minkowskian) spacetime: in the old view, time was something separate and distinct from space:
Now, in the modern view, time is another kind of thing that’s just like space.
Read on if that doesn’t say it all.
You know how left-right and forward-back are only relative to some axis system? Like if you turn to the left, then left-right are different. Also if you lie down, then up-down are different. Well, sooner-later is the same kind of thing as left-right. If you go really fast (like 10% of the speed of light) then you notice this.
Going this fast relative to me, your time will be slower than my time — your watch will literally run slower. Just like, if we were facing the same direction, and I turned 10 degrees to the left, then our “forwards” would be different. Which means, walking at the same speed I would achieve less “forward” than you, according to your “forward”.
SOURCE: Sean Carroll