Time, as we currently understand it, is best thought of as an extra special dimension. Just as space can be thought of a certain kind of relation between objects, so can time. Thinking about time in this way leads naturally to the conclusion that the past and the future are equally real, it just doesn’t make sense to think of things as “moving” through time, or that somehow the future comes into existence when needed. For more explanation of these ideas see here and here.
But if it really is the case that time exists “all at once” then why do we experience ourselves as “moving” through it, with one special moment, the now, distinguished, separating the future from the past? And why do we experience time as moving in one direction rather than the other? (An especially tricky question, given that there is no “arrow of time” in the physical laws, causation could equally well be described as working from future to past.)
Before I address the questions directly, consider what would happen if between one moment and the next some large number of duplicate moments were inserted. Since the mind is something that is in the physical world (by assumption) there is no way that we could be aware of the duplicated moments, and thus our experience of time would be exactly the same as it would have been without the duplicated moments. This should be at least give us the right intuitions, that the “flow of time” that we experience is something that is created by the operation of the mind, and not something that exists independently of us. (Although the temporal relations do exist independently of us. I am not trying to assert here that time itself is a construction of the mind; that would be silly.)
The key to understanding our perception of time as something that we travel through, with a distinguished present, is memories. In any given moment we have memories of the immediately previous moments, perceptions of the current moment, and no knowledge of the future. Any conscious mind always has a “current” experience (including perception), and this is simply a feature of consciousness, for to be conscious is to experiencing, and there is only room for one unified experience (even though one can remember past experiences the remembering is presented as part of the current experience). And consciousness is necessarily structured in this way, any consciousness, at any time, is experiencing something, which will be different at different times. Information about events occurring at the same moment will be incorporated into that experience, if that consciousness is to be able to react to those events, thus incorporating the yielding that the experience is happening at the same time as certain events. And, of course, at any moment in time a different experience is “current” for a given mind. So, since past experiences are available in memory, with the knowledge that they were at one point experienced as current, it is not hard to see how the impression that there exists a now, which corresponds to the experience that is being “lived through” at the moment, which will “later” be only remembered (in future moments it will be available to consciousness only a remembering that is part of some other current experience). This naturally leads to the division of time into a past, which can be remembered, a present, which is being experienced, and a future, which one has no knowledge of. And because our memory allows us to know that at past times we divided the time into past, present, and future differently it is natural to assume that somehow time is changing, or that we are moving through it, in such a way that the current experience really is special and distinguished, the past really is “behind us”, and the future is non existent. Obviously then we make a mistake when we impose the structure of our experience of time on time itself, but it is an understandable mistake.
This leads me to the second question I posed above: why do we perceive time as moving from past to future, and not vice versa? One possibility might be because of the way causation works, but unfortunately this answer, however intuitive it might seem, doesn’t hold water. We know that the physical laws could equally well operate in reverse*, and thus all of our causal laws could be converted into laws of evidence, and our laws of evidence into causal laws. The real reason I suspect has to do with entropy. As you are probably know entropy always increases (at least in the direction of time we think of as “normal”). This means that in our direction of time it is possible for organized structures to be created, as processes can use the movement towards greater entropy to build complex structures (if you want more detail than that I suggest you find a physicist). Evolution, for example, happens only in the “normal” direction of time; we don’t witness complex structures being replaced with simpler versions of themselves over long periods of time (which is what we might expect to observe if evolution could run in the “opposite direction”). For similar reasons information also accumulates only in the “normal direction”. And because information collects only in the “normal direction” if a creature with a mind is able to experience the flow of time it must experience it going in our direction, since it couldn’t have memories that would support an experience of time as working in the other direction.
I should emphasize, again, that temporal relations and causation are real, they have an objective existence that is independent of people. The division of time into the present, past, and future is, however, a construct of the mind. We do not move through time, there is no special “now”, and future moments are just as real as every other moment. Even so, I don’t advise trying to think “timelessly”. Giving more attention to the current experience is important for one to properly respond to events, and even though the future is as real as the present there is no way to get any information about it. I say this because it is important to make the distinction between the philosophy of time, which is thinking about the nature of time, and mystical nonsense, which is encouraging people to be timeless consciousnesses (whatever that means); even though there is no special present moment it is most effective to act as though there were one.
* Actually, if I remember correctly, there is a certain type of fundamental particle whose laws can’t be reversed in time, but is unlikely that these particles are responsible for our conscious experience of “time’s arrow”, since there is no reason to believe that the operation of the brain is designed to be sensitive to them.