Physicist’s ideas of time
qz.com
qz.com
General Relativity have some definition of time locally, that is more complicated than the time in Special Relativity.
The problem in Special Relativity is that time is not the same for every observer, because if you are moving the "time" you see is different than the "time" I see. Anyway, you can convert your time to my time or vice versa using some clear small math formulas.
In an abstract setting, it's essentially the same problem that right and left have. Everyone has a different definition, but you can convert them. For time the conversion looks more weird because in usual conditions you can approximate that everyone has the same time and live happily, but it is only an approximation.
In General Relativity the space-time is curved, so it is more difficult to do the conversions. It's more difficult because the math is more difficult and because you must stich the times from different parts, so there are real problems to stich them. If you like bad analogies, it is the same problem that make so difficult to make a good planispheres. Drawing the spherical surface of the Earth in a plane cause problems. https://xkcd.com/977/
In Special/General Relativity, the universe is made of "events", they are like the "points" in a plane but instead of having two coordinates like (x, y) or three like (x, y, z) they have four coordinates like (t, x, y, z). (For technical reasons, you will be happier if you multiply the time by c and use (ct, x, y, z).)
Each point in a plane exist on its own, but it is easier if you add some differentiable structure and consider that the point (7.9999999999, 4.00000001) is "close" to the point (8.0, 4.0). In spacetime you can add a similar structure to the events with four coordinates, but there are some technical details because time is special. But it is not much more surprising than defining the nearby points in a plane. In General Relativity the curvature make everything more complicated, but not mind blowing.
I think the article mix the thermodynamic arrow of time to increase the confusion, but if you want to understand the problem it's better to read https://en.wikipedia.org/wiki/Arrow_of_time