What is a clock, what is a "good" clock, and why do any good clocks exist?
A clock is just a physical system which goes through a repeating cycle. The cycle can be anything from the swinging of a pendulum to the vibrations of the electromagnetic field. By counting the cycles we can attempt to measure of the passage of time.
Of course our measurements won't be very useful unless the time taken for each cycle remains constant. A clock whose cycle time remains constant is a "good" clock, and we really need at least one of these to make any sense of time at all.
Fortunately, we can expect almost any reasonably-constructed clock to be good, in almost any reasonably-imaginable universe. The reason for this is that the laws of a reasonable universe have a symmetry known as "time translation invariance", which is a fancy way of saying that the laws today are the same as the laws tomorrow. This means that identical starting conditions give rise to identical evolution, regardless of time. Since each clock cycle starts with an identical configuration, each clock cycle unfolds the same, and takes the same amount of time.
How do we know that this "time translation invariance" is actually true? We don't know for sure, but it is true for our current best-guess theories, and it is hard to see how life or any interesting structure could evolve in a universe without it. Evolution couldn't work if the next generation was subject to different laws from the current one - and the Earth itself probably could not sustain a regular orbit around a star.
So time translation invariance is a very fundamental assumption/observation of physics. Perhaps it is not surprising then that it is intimately connected to the most fundamental quantity of physics - energy. Energy conservation is the flip side of time translation symmetry. Mathematically they are simply different statements of the same thing; but this will have to be the subject of another post.