Without going much into detail the Vipassana meditation technique is actually a very simple technique, at least the beginning stage that you learn during the first 10 days retreat. The only thing that you do is witnessing the gross and subtle sensations of the body without having any positive or negative reaction to it, without having attachment or aversion to any experience, without creating any cravings for any experience, or in other words without expecting anything.
This is called the practice of "Equanimity" and it is developed by becoming a witness of the experiences and understanding "Anicca" (pronounced Anitcha) impermanence. Since no body sensation (gross or subtle) is permanent there is no reason to become attached to any experience.
As I understood from the lectures this simple process of witnessing the sensations of the body from head to toes and toes to head with equanimity helps to purifies the mind. By observing the gross sensations of the body you later start experiencing more subtle sensations like tingling, the feeling of flowing energy, vibration, energy waves and even later this can lead to a stage called the "dissolution of the body" where the body feels like exploding into tiny particles. There is no more a feeling of a physical limiting body anymore.
This "dissolution of the body" is the main experience that they try to reach to. By having this experience again and again and going deeper into it it should allow us to realize the deeper truth that we are not the body nor the mind. But, although you are looking for this experience you are not really looking for it cause you know... you should be just a witness of any body sensations without any sense of craving or aversion.
And by practicing equanimity, avoiding creating any feeling of aversion or attachment little by little we stop creating new Samskaras (mental habit patterns of aversion and attachment) and the previous Samskaras are able to come up to the surface from the subconscious to the conscious to be finally extinguished. This is a life long process.
Well, this is what I understood from my first Vipassana retreat so I'm definitely not an expert. Maybe is better that you hear from Goenka himself about the Vipassana Technique in the two videos below available in YouTube. You can also read about the technique in there official website: What is Vipassana?
Introduction to Vipassana by Goenka
Vipassana viewed from a Yoga philosophy perspective.
I like to see this technique from a different point of view. While practicing meditation you should always practice equanimity, regardless of the meditation technique you are following. If there is no equanimity and a positive nice experience arises during the practice of meditation then we will get excited. This excitement will stimulate again the breathing which had already become very serene thanks to the meditation process but now becomes agitated which in turn stimulates the heart rate. So whatever experience was there it goes away because the mind and the body become easily agitated. But if we are able to remain still, calm, serene without any expectation and without any feeling of craving or aversion to whatever experience might arise then we could go deeper into such state until it naturally fades away.
The subtle body sensations: Prana, vital force or energy
According to yoga philosophy there is a certain subtle energy that pervades the whole creation. It is in the air that we breath, in the food that we take and in our own physical bodies. This energy is called Prana, the same energy known as Qi or Chi in Martial Arts. This energy is more subtle than electricity, it cannot be measured but it can certainly be experienced.
The prana in the physical body is that energy that allows the body to perform its different functions like breathing, digestion, procreation, sneezing, coughing or even crying. It is divided in five type of pranas (the Pancha Pranas) according to the function that it performs. One of this pranas is called Vyana which is the prana that pervades the whole body.
There are yogic practices similar to Vipassana where one works with Vyana Prana. By simply putting the attention to any body part the prana can be felt as subtle sensations and by moving the attention or rotating the awareness around the body we stimulate the flow of this prana. This process of scanning the body and feeling the prana (subtle body sensations) in each body part stimulates the flow of prana and it removes energy blocks on the pranic body which is nothing but mental blocks.
It is also said that the grossest manifestation of prana is the physical body and the subtlest manifestation of prana is the thoughts, the thinking process and the mind. So the connection between the mind and the physical body is prana itself.
This little comparison just helps me to understand Vipassana and why they say that this technique purifies the mind. Now it is important to mention that Goenka says "we should not play with the subtle sensations of the body but just observe them with equanimity, otherwise we are going back to the same old habit pattern of creating aversion or attachment". I find this difference between observing and playing very subtle. According to Yoga this very process of moving the attention from head to toes and toes to head moves the energy or prana in the body "Wherever the mind goes the prana flows".