Speed of light, why is it about time dilation? I've watched several video's on this topic but I've never seen the relation between actual time and the "time dilation" that is happening.
As an example this video, start around 6 minutes and 27 seconds:
https://www.youtube.com/watch?v=yuD34tEpRFw
It explains how different observers would measure the same second on the falling man differently. The way I interpret this isn't that time itself is different per observer, but the difference in speed at which the observed object can change it's state from one moment to another.
Yet everyone and everything says it's about time. Period. Nothing else. Why is this? The light experiment shows very clearly that it is the falling man that changes slower or faster depending on the observer. So time dilation would be a factor of how fast an object can change the same state to another state. Say a specific single chemical process on the observed object compared to the same chemical object on the observer.
 A: First of all, your observation is exactly right: it is "the difference in speed at which the observed object can change it's state from one moment to another" and "a factor of how fast an object can change the same state to another state. Say a specific single chemical process on the observed object compared to the same chemical object on the observer." Yes. This is exactly right.
So now let me expand your example a bit. You mentioned a chemical process. It goes at a different rate. How about a nuclear process? That will go at a different rate too. What about simple mechanical things, springs and so on? They go at a different rate. And biological stuff? Heart-beats, neuron signals and synapses? All go at a different, slower rate. ALL these things are slowed, and all by the same factor. And this is precisely what is meant by the phrase "time dilation". It is called time dilation, rather than "physical process slowing" simply because when all the physical processes slow, and all by the same factor, it seems appropriate to attribute the slowing to a concept not pinned to any one process, so we use the word "time". But in the end this is just a way to refer to what physical processes are doing.
(In order to prove that everything slows, and all by the same factor, one makes an appeal to the principle of relativity, which asserts that the physics within a frame moving along with any given moving body or set of bodies will be unaffected by this shared inertial motion. It follows that all the processes stay in step with another as they all move along together.)  
A: These two ways of thinking about it are pretty much equivalent. If an observer measures an object changing slower, they measure a greater time interval between changes, so they measure time to pass slower for this object.
I'm not sure if this is what you asked but I will include it: If only one specific change was slowed then the postulates of special relativity wouldn't hold. The moving observer could carry out two processes, one which is slowed and one which isn't, and determine whether or not he is at rest.
A: What is time but a measure of changes that are happening to an object? Time is not some real object that we can directly observe. It is parameter that tells you the speed at which processes happen together with prescription of how to compare the parameter between different objects. 
Every event that ever happened or will happen in the universe can be put into a set. Now, because of causality, there exists chronology between these events. For example let us have 3 events:
1.) John sees a ball and start running toward it
2.) John reaches the ball
3.) John kicks the ball.
4.) John scores a goal
The later event is always consequence of the previous one so there is natural way of organizing all this events into chronology of the type A->B->C->D->.... Now, you can give every event in this chain its own number in ascending order, as I did in the enumeration above, which will uniquely define the event in the chain. So for example event with parameter 3 in this chain is event John kicked the ball. And since changes are continuous this parameter should be also continuous. So for example event with parameter 2.5 of this chain should be some event of the type "John halfed the distance toward the ball".
Now there are many chain of consequences all of them interconnected together. F.e. you could follow the chain of events of the ball to the point where the John kicks the ball, where the two chains meet. After that, you could pick wheter the chain will continue to follow the ball, or skips to follow John. And every such chain will have its own parameter.
Now, in real universe, there is a prescription how to naturally synchronize all this paramaters (in special theory of relativity this prescription is global, in general relativity it is only valid locally, in both cases for chains of events that are "inertial"), so that you will end up with only one parameter called time. 
From physical point of view, this time should be given by some real process, that we consider to be as periodical as possible. Because speed of light seems to be constant everywhere (in vacuum) and in every direction, we can construct device in which light bounces back and forth and this process will be perfectly periodical. Thus time is nothing but a rate at which light bounces back and forth on this clock, and relative rate between two such clocks depends on their relative movement. 
One could wish to synchronize this parameter with different prescription, so that time does not depend on the reference frame. This was done before Einstein, but such prescription proved to be problematic and led to complicated theories of eather just to describe simple thing like how the light propagates. It turned out, that the natural way to define time is indeed with light propagation and so we are stuck with time dilatation by DEFINITION of what the time is. And this proved to be the most usefull definition of time everyone was able to come up with. 
A: The speed of light is used to formulate time dilations because it is a constant, in a vacuum it's speed is always the same for any observer. Most chemical reactions, as you seem to suggest using, are not always time invariant, as different factors may affect them.
