What is the difference between relative and absolute truth in Buddhist philosophy? Many Buddhist texts and teachings make a distinction between absolute and relative truth. Please explain the difference and give some examples.
In Theravada, as the Wikipedia article states, there are types of truth: conventional truth (sammuti-sacca) and ultimate truth (paramattha-sacca).

These two types of truth are not exactly the same as relative and absolute truths. Rather than focusing on the universality or specificity of the scope of the truth, they focus on the intrinsicness of the truth - i.e., whether an object agrees with a truth by its inherent nature, or whether it is simply said to agree with it by external convention.

An example of conventional, extrinsic truth is in a fist. When you close your hand, a fist appears, almost by magic. When you open your hand again, the fist disappears. There was never anything intrinsic about the object that made the fist appear; only convention and recognition gave rise to the truth or falsehood of the arising of a fist.

An example of ultimate, intrinsic truth is in the pain felt when a fist connects at high velocity with a face. The fist and the face are only conventional descriptions of the reality, but the pain is intrinsic to the experience and thus said to be ultimately real. Also ultimately real are the vision of the fist coming towards the face, the feeling of the hardness of the fist and the softness of the face, and the sound of the fist connecting with the face.

In brief, conventional reality refers to entities, while ultimate reality refers to the building blocks that make up reality (i.e. experience). So, the entities of fists and faces are conventional, but the sights, sounds, and feelings associated with the experience are ultimate reality.

The importance of this doctrine is in establishing a proper paradigm for understanding reality. Because conventional truths are based on mental formations, they cannot aid in an understanding of reality. A permanent, satisfying, controllable convention can be conceived of, but it will never exist in ultimate reality. By delineating that which exists in ultimate reality, one can limit one's observation to those objects that will provide an understanding of how reality works.

For example, focusing on the concept of food as you eat, you will never come to see the nature of reality as arising and ceasing incessantly, because you are focused on something that is constant (but not really existing) - i.e. the food. As a result, you will easily conceive of it as good or bad, me and mine. If you focus on the experience of tasting and feeling as you chew the food, you will notice that you don't actually taste or feel the food always, your mind flitting between tasting, feeling, liking, disliking, thinking, etc., and you will come to understand the nature of reality, which in turn will allow you to let go of your attachments to good an bad experiences as you see that there is nothing truly desirable or undesirable about them.

This is based on the teaching of the Buddha while he was alive.

Relative and absolute truth, I believe, are more a part of the Mahayana claim that the teachings of the Buddha during his life were only meant to be taken in the context of the audience's limited ability to understand higher truths. Such teachings, it is claimed, can therefore be disregarded or at least superseded by later teachings that were kept secret until a time when beings could understand the higher truths they contained. 

So, an example of a relative truth would be the teaching of dependent origination and the four noble truths; ultimate truth would be seeing that even those teachings are emptiness, and therefore meaningless. The point is that in order to understand the ultimate truth of emptiness, one must first realize the conventional truths as stepping stones.

I'm sorry if I haven't done the Mahayana view justice, but I don't subscribe to it myself; there is nothing in the original teachings of the Buddha to suggest that they are only relatively true, or that there is anything absolute beyond them. But, I guess I'm biased :)