Philosophy Now magazine has a "Question of the Month" section which asks a question from readers and they can submit their answers to the magazine. Philosophy Now will select and publish some of the answers.
Issue 153 "Question of the Month" was "What is Time?" I submitted my answer but it didn't get published as selected answers in issue 155. I decided to publish my answer here (without changing it) and discuss a bit about the selected answers.
What is Time? - My submitted answer
Sometimes I think of Time as a labeling system of universe states or some easy uniquifier.
The universe is constantly changing and we can sort of divide it into multiple states. One of these states, Call it "S1" for example contains that the sun is in the middle of the sky, I'm behind my computer, etc. The other state "S2" is that the sun is rising, I'm in my bed, etc. Now if I want to know more about S1, Like where was John in S1? I will ask him "Where were you when the sun was in the middle of the sky?". Here I'm using the sun as specifying and referring to the state that I want to know John's position in it.
You can see that finding a common state uniquifier (or label/name) between me and John for referring to a specific state is not always easy as using the sun position. Time is the thing that will become part of the state and is a good uniquifier for pointing to a specific state. I can ask John "Where were you at noon today?" and the answer to that will give me information that I want.
You may say that this isn't the answer to the question. Even on asking "Where were you when the sun was in the middle of the sky?" the concept of time exists. I get your point.
Time at its core is any uniquifier of the universe state that we use. So anything that is used for referring to a specific state could be time. Time is somehow the label or name of the state. From now by Time I mean any general uniquifier and by Time System I mean the official time that we use daily and it's extracted by our clock and calendar.
The official time system is util created by humans as an easy objective state uniquifier between themselves. It also shows the order of state regarding other states. So by using the official time system we will know which state had come first.
To wrap it up. The universe is constantly changing, We can divide it into different states. Time is the thing that we use to refer to a specific state. The official time system is an easy objective uniquifier that also shows the order of state regarding other states.
On accepted answers
You can see and read accepted answers here. I will make some notes on the answers that caught my interest.
If you take time and change the same thing as I did in my answer, which of course I'm not sure of. Saying something like "Time does not exist without change" or "Time needs to exist for change to happen" doesn't make sense as they took Time and Change separate things.
I'm not familiar with special cases of time in physics, But Richard's notes on Einstein's theories of special and general theory of relativity are cases that understanding them widens my intuition and definition of time should explain those too. At last, maybe time is a different thing from change.
If it is the case that Time and Change are separate things. Then for me, there is a question from which we go to another. Is it time that shows us change or the other way?
The first time I saw the idea of observing events all at once was in an argument that was defending compatibilistic view of free will and God's knowledge of the past and future. The argument was saying that god is timeless and all the events all at once are some sort of like in front of it.
Spacetime landscape as it is interesting it is also hard to understand for me. All moments (past, present, future) co-existing in a timeless state is something I can't get it yet.
Anyone saying that time doesn't exist without the observer, I don't get it if the same thing won't be true about space too. From what Nella points out Kant it seems he believes that both time and space won't exist without the observer.
I think I get how time is a precondition of experience as Kant says so. Perception means change from a state you weren't aware of something to being aware, I can't find it possible perception without change in perceptor. And if we take time and change the same thing or at least tied together then time is a precondition of perception. But still from this point of view, it doesn't mean there won't be any time (or space) without any observer. It seems to me conceivable change without the existence of any observer so then there will be time without any observer.
I find Mike's answer close to my definition of time and it's well said in comparison to my answer. Still, it's a question for me that can this notion of time explain special and general relativity and other non-intuitive cases in physics?
Identity and Time
Other thing I liked to note about time and its relation to identity. For me, it's hard to conceive identity without time. I think we get the notion of identity by connecting the dots between objects changes (time). So with a timeless state I don't see how identity means anything.