Why do we perceive time? Since everything (at least what we observe) is travelling through the time in the same direction and speed why do we even perceive the time? Of course, there is the time dilatation, but it is negligible between you and me, for example. If it is so, why do we even observe the effects of time when we do not observe changes of something which is moving through the space with the same velocity (or a little bit different) as we do?
What is the difference between existence and non-existence of time? What is the difference between time and space?
 A: Once you ask about perception, it is no longer physics question.
Anyway we do not percieve time. Look around and all you will see is present moment. The time is abstraction given by the memory of changes that were once happening. And to derive from this memory the flow of time is an abstraction. All the percieved memory is here and now, but there are also links that connects which events predated the next.
Take for example a diary. You know that one event was sooner than later because the later is written on the next page. From that you abstract away the flow of time.
Now to return to physics:
The time is defined by its measurement, and we choose such definition to make physical laws as simple as possible. So let us have some clocks, that have such a period of repeated events, that we are satisfied to call the time intervals between those events as same, f.e. pendulum.
to say something happened at some time, you will say the n-th click of the pendulum and the event happened at the same time. Then you write down to your diary (or better yet - lab report) at this click this happened. At the end of measurement you have huge diary with a lot of associations between clicks numbers and events. If the events are position (x) of some object, then you have graph $x(n)$. By defining time interval between two clicks f.e "1 second" you can get graph of position vs time $x(t)$ and then seek the laws that are consistent with the graph, f.e. $F_g=m a$, where $a$ is acceleration of the object, $F_g$ gravitational force and $m$ mass of the object.
In Newtonian physics saying that something happened at same time as click of some ideal clock is absolute. Einstein however realized, that this notion is absolute only if the two things happened not only at the same time, but also at the same place. Then you can say they happened at the same time, because you have seen them both happened at once. If they are not at same place, you must adjust for light speed and here all of the magic of special relativity comes in. 
So time in physics appears only as a set of data together with their relations to clicks numbers. But the data are always percieved whole at any moment, you never see any past or future or flow of time anywhere.
A: You are able to detect a change in things around you — that an egg can break, the sun can rise, a colour can fade. So, you can detect different states of things. And those states are obviously not all present simultaneously. What should we call this "phenomenon", this "feature" of the world? We call it time.
The fact that everything doesn't happen at once, is given the name: time.

Source
So, it is not obvious when you claim that "everything [...] is travelling through the time in the same direction and speed". Because time is only noticeable when things change. Hypothetically, if everything was slowed down equally much - all events and behaviour, all chemical reactions - then we wouldn't notice. Because what we measure time from - the changes in our surroundings - would have been slowed down just as much as our perception.
You seem to be aiming towards the conclusion that we shouldn't be able to notice anything changing since we all move equally fast through time. But this idea is an upside-down way of thinking, because if we really couldn't detect changes, then we wouldn't have had a need for a concept like time in the first place.
A: Some things to consider:


*

*Humans exist because we evolved over time. That is, humans at time A makes it more likely to find humans at time B, because we reproduce.

*If we evolved over some other dimension, might we perceive that dimension as time? I don't know.

*Our brains have components designed to measure time. We know from daily life that time perception has functional utility.

*It is not hard to imagine how an object within time can nevertheless perceive it. A pendulum clock "perceives" time through a differential equation that relates position and acceleration. It "remembers" the time because the gears in the clock advance only in one direction with each pendulum swing.

*If you stretch your imagination, maybe you can say the ocean "perceives" space by the variation in pressure from floor to surface. Like the pendulum clock, it creates a variable that varies over the dimension to be measured. Whether this counts as perception depends on how you characterize it.
A: I presume you are indirectly referencing the idea that time does not exist - i.e., that if there could exist an observer outside of our universe then they would see a completely static space. One way that this is resolved was taken up by Page and Wooter: According to Page and Wooter, time is essentially the result of entanglement between 2 spatial systems, wherein one is called a "clock." (Note that this idea of a "clock" does not say that time exists for an "external observer" but that it exists for anyone within the universe.) The clock system has been essentially discussed in the other answers, so I shall not add to that information. Instead, I shall mention some of the implications: This idea of a "clock" allows the definition of a time operator (which is not necessarily Hermitian) within quantum mechanics. This has measurable effects such as a correction to time dilation due to quantum mechanics (this was recently reported on in Nature Physics). I would suggest you refer to the paper "Quantum Time" (see https://journals-aps-org.prox.lib.ncsu.edu/prd/abstract/10.1103/PhysRevD.92.045033) and various papers that cite it, as well as the original Page and Wooter paper cited in "Quantum Time" (see https://journals-aps-org.prox.lib.ncsu.edu/prd/abstract/10.1103/PhysRevD.27.2885).
