In his book Insight Meditation: The Practice of Freedom, Joseph Goldstein offers the following introduction to Insight (Vipassana) Meditation practice:
The insights of insight meditation are intuitive, not conceptual. Intuitive in this sense does not mean some kind of vague feeling about something; rather, it means clearly, directly seeing and experiencing how things really are.
For example, you are sitting in meditation, watching the breath. All of a sudden your mind settles into a different space. Even if it is just for a couple of moments, you feel a deeper kind of calm and peace. Instead of struggling to be with the breath, you begin just to test with the breath in a very calm, effortless way.
That is an insight through direct experience into the nature of calm and tranquility. You do not think about them or reflect on them. You know that daffodils are yellow because you have seen them. You know the nature of calm and tranquility because you have felt them in your heart.
- Page 53
Today, this brief video from www.dhamma.org provides an introduction to this practice: