One of the two major types of meditation in Buddhism, along with metta (loving-kindness). Its purpose is to lay bare the nature of reality by developing mindfulness. Simply put, as one meditates in this fashion, they come to realizations as to the true workings of the mind, thought and experience.
To begin, sit in a comfortable position - the lotus position is the most widely used, but it can be uncomforable for beginners. Start by focusing your attention on a single item in your awareness. A good thing to use is your breathing. As you draw your breath in, try to consider the experience carefully, being mindful of the physical sensation of the rising and falling of the chest, as well as the feeling as the air passes over your nostrils or your lips.
When you begin, you may find it helpful to count each breath. Counting the breath makes it easier to focus your concentration on the breathing and to keep your mind from wandering. In your mind, simply count "one" as you breathe in, "two" as you breathe out, and so forth. You will find, most likely that it is very difficult (at first) to reach ten without having your mind wander away from you. When you find that this happens (and it will), do not worry or become upset. Simply recognize that your mind has wandered, and begin again from "one". Another similar thing which might happen is that you will count far past ten without ever realizing it. Should this happen, do the same as you would do if you found your mind wandering before reaching ten.
It is important to note that the purpose of counting the breath is not to reach ten. That number is arbitrary. The purpose of the activity is to learn to control your mind; to keep it from wandering.
As you develop in your meditation, you will eventually come to understand reality as it actually is. You will come to understand the Four Noble Truths, karma, rebirth, and the empty nature of self and of thought.
Meditation practice leads to a more peaceful existence and, eventually, Enlightenment.