This section about meditation from Awakening the Buddha Within: Eight Steps to Enlightenment: Tibetan Wisdom for the Western World by Lama Surya Das is a great introduction for Westerners:
Awareness, Attention, and Focus
Westerners who are attracted to Buddhism because of meditation often make the mistake of seeing meditation in the narrow sense of going into a quiet room, crossing your legs, and closing your eyes. What the Buddha actually intended by this part of the path was mental discipline, an effort to train the mind through the cultivation of mindful awareness and attention to the present. If all the difficulties of life are the result of ignorance, deluded thinking, and conflicting emotions, then the obvious solution is to get wiser, more aware, balanced, and loving. We do this through the practice of meditation training or samadhi. Meditation training includes Right Effort, Right Mindfulness, and Right Concentration.
Demystified and divested of religious and cultural trappings, meditation basically means the intentional cultivation of mindful awareness and pure attention — an alert, wakeful presence of mind. This development of awareness eradicates ignorance — about ourselves and others as well as reality. Meditation awakens and frees the mind, and opens the heart, helping us develop inner wisdom, clarity, joy, and compassion, thus bringing spirituality and a larger perspective into every aspect of daily life. Meditation training helps us to concentrate as well as to see and think more clearly. In this way we develop spiritually into wiser, more selfless, and caring men and women.