There are two distinct topics here, about time and the arrow of time.
The universe is a 4D space in which matter resides, and because of the geometry of space and the nature of matter, the matter apparently takes the forms of wiggly lines/curves that all tend to extend in roughly the same direction, between 'past' and 'future' ends of the universe. This direction is called 'time'.
So to answer the question "What is time?" it is helpful to first consider the question "What is space?" It's essentially the same question, but probably easier to answer because it's not confused by some of the odd-man-out features of time. For some reason, it seems to evoke a lot less interest.
Space has a bunch of geometrical concepts like 'length' and 'angle' that we can then extend to the time direction to build concepts like 'duration' and 'speed'. This is really just geometry. "What is space and why does it have these geometrical properties?" is deep and mysterious, but having accepted that it exists, figuring out the consequences of its rules is just routine maths. 'Duration' is no more mysterious than 'length', 'clocks' no more mysterious than 'rulers'.
The question "What is the arrow of time?" is really a question about the behaviour of matter in the universe - the shapes of those wiggly lines. The arrow of time is what allow us to have memories, and drives thermodynamic progress. It is also more complicated and mysterious.
If we consider all the possible configurations matter might take, almost all of them look like nothing is happening. It starts random, ends random, and is random at every point in between. It's a box full of particles bouncing around, endlessly. There is continual change at the microscopic level, but it always changes into something that looks very similar. And if you play the tape backwards, it looks just the same.
Our universe is extremely peculiar in this regard in that that patterns matter makes at one end (the past) are extremely well-ordered and non-random. Nobody knows why. The odds of it happening by chance are mind-bogglingly low. It no doubt has something to do with the physics of how the universe started. But so far as I know, nobody has come up with any plausible explanation as to why.
Given an ordered past, the most likely way for matter to behave is to spread out randomly into the future, like holding a bundle of fine threads in one hand at one end, and letting the other ends blow in the wind. This gives us our irreversible processes, and we can harness the progression from order to disorder to drive useful machinery (like clocks and organisms). The progression to disorder impresses the past behaviour of a thread on its future, but not vice versa, so we only have memories of the past and not the future. This in turn gives us the illusions of 'moving through time' and 'living in one moment'. Most of our philosophical questions about time arise from the constrained perspective this gives us.
Unfortunately, the ultimate answer to our questions is still lost in the distant past. In the part of space and time we can see, we can trace back all the peculiar properties of our perception of time to this business of the matter being far more ordered than we have any right to expect at the past boundary. But as we look further and further back, the question just gets pushed back too. We know of no way that order of such magnitude can arise spontaneously. We cannot create it. (Devices like refrigerators only move it around.) All we can do is exploit the order we have inherited from our unknown past.
In summary - I think you are really asking about the arrow of time, and that question is not really about time itself but a property of the history of matter, evolving in time. However, it's probably true to say that it's the source of a lot of our questions about our experience of 'time', which is what we often mean by the word. So a case could be made for either answer. It depends what aspects of 'time' you're talking about.