Previous answers don't provide a philosophical approach of time, so here's one.
Perhaps the most important perspective of time comes from the philosopher Immanuel Kant, as expressed in his Critique of Pure Reason. The definition actually requires a bit of context.
At the time Kant wrote this magnum opus of philosophy, philosophers were debating if knowledge comes from reason (rationalists sustained that one can know everything just by learning and thinking, practically independently from the senses), or it comes from experience (empiricists sustained that all knowledge comes from experience, which is essentially provided by the senses).
Immanuel Kant proposed a key question to solve the issue: How is synthetic a priori knowledge produced?
a) Synthetic means that is pure knowledge, not coming from a definition (for example, the word bachelor already suggests that the individual is not married, so, saying that bachelors are not married is not pure knowledge, it is analytic knowledge);
b) a priori means that it does not come from experience (e.g. we have never experienced a triangle or a number, but, mysteriously, such concepts exist in our mind; Kant calls this type of knowledge a priori). Notice that a priori does not mean previous in time. It is moreover the expression of a dependency: in order to add apples, we need the a priori concept of number; that is, addition is dependent on the a priori knowledge of numbers.
Time is precisely a case of synthetic a priori knowledge: it is synthetic (a pure concept, not derived from other), and it is a priori (we don't need the senses to know time, it is something that we just know, independently of experience).
So, Kant proposed an answer to the mysterious raising of such types of knowledge in our mind: we create them subjectively in order to make understanding possible. For your question, this means that time is a subjective production, that allows understanding possible; time is not a feature of nature; it is something that exists only in our mind. Later philosophers, in coherence with Kant's approach, tend to suggest that time is just a sequential order by means of which we organize knowledge in our mind. For example: we know the entrance, we know the hall, and we know the desks of our office, but in addition, they are ordered, so we have an experience of them in time. From a blunt perspective, time is just memory and space is just movement.
For Kant, time and space are subjective productions. Kant starts his book with this, so it is perhaps worth a read.
Now, you might say "ok, but time and space are physical concepts, Einstein's relativity would not be possible if they would only be subjective constructs". If so, you are partially right: metaphysics does not depend on science: it is the opposite.
Let me explain. Science does not search final truths: it just search for empirical truth. The branch of knowledge that deals with final truths is philosophy. So, science is absolutely dependent on our senses.
This is easier to understand with an example: temperature is not an attribute of nature (in fact, not even things exist in nature, everything would be something like energy); temperature is just a feeling, a property of what we call an object, some portion of nature. So, in order to find the relationships between temperature, pressure and volume, three laws of thermodynamics were developed. At this point, scientists noticed the problem with temperature: what is exactly temperature, excluding the concept of feeling? So, they added a law which provided the concept of temperature, that needs to be previous to those already existing for them to be true, so it was called the zeroth law of thermodynamics, which precisely defines what temperature is. With that, thermodynamics has all the elements of a science: a knowledge that describe some behavior of our experience.
So, time in physics is a concept that is dependent on our experience (anyway, there's no other way of knowing it). Physical time is a mathematical formalization of our knowledge, like temperature in thermodynamics. But we can't say that time and space are final truths. We just can't know nature in other way than by means of our senses and reason.
Kant's concepts of time and space are probably those which are still influencing the most on the making of science. For example, Google for "Kant quantum mechanics" and you'll see the importance of his approach of time and space in contemporary science.