How do the Chakras relate to Kundalini? And what is Kundalini?

First of all, what is Kundalini?  Wikipedia describes Kundalini as a sleeping, dormant potential force in the human body.  It is a component of what is described by many as the "subtle body", that energetic component of who we are outside of the physical.  The subtle body consist of nadis (energy channels), chakras (psychic energy centers), prana (subtle cosmic or Universal energy), and bindu(drops of essence or consciousness).   The Bindi is a small ornamental dot applied to the forehead of females in Hinduism.

 Kundalini is described as being coiled up at the base of the spine and is said to reside in the triangular shaped sacrum bone in three and a half coils.

The Sanskrit adjective kundalin means "circular" and also occurs as a noun for "a snake" meaning that it is coiled and forms circles.   As this sleeping or dormant "snake" it resides in all of us as our potential that can be awakened by a Guru or teacher or by spiritual practices like yoga or meditation.  As it is awoken it progresses through the different chakras leading to different levels of awakening.  This is how they Chakras are related to Kundalini in Hindu tradition.

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From the Wikipedia entry for Kundalini I found the following:

Swami Vivekananda described Kundalini briefly in London during his lectures on Raja Yoga as follows:

According to the Yogis, there are two nerve currents in the spinal column, called Pingalâ and Idâ, and a hollow canal called Sushumna running through the spinal cord. At the lower end of the hollow canal is what the Yogis call the "Lotus of the Kundalini". They describe it as triangular in form in which, in the symbolical language of the Yogis, there is a power called the Kundalini, coiled up. When that Kundalini awakes, it tries to force a passage through this hollow canal, and as it rises step by step, as it were, layer after layer of the mind becomes open and all the different visions and wonderful powers come to the Yogi. When it reaches the brain, the Yogi is perfectly detached from the body and mind; the soul finds itself free. We know that the spinal cord is composed in a peculiar manner. If we take the figure eight horizontally (∞) there are two parts which are connected in the middle. Suppose you add eight after eight, piled one on top of the other, that will represent the spinal cord. The left is the Ida, the right Pingala, and that hollow canal which runs through the centre of the spinal cord is the Sushumna. Where the spinal cord ends in some of the lumbar vertebrae, a fine fibre issues downwards, and the canal runs up even within that fibre, only much finer. The canal is closed at the lower end, which is situated near what is called the sacral plexus, which, according to modern physiology, is triangular in form. The different plexuses that have their centres in the spinal canal can very well stand for the different "lotuses" of the Yogi.

In some Hindu traditions, the Kundalini is perceived as the Goddess Shakti (the feminine, creative power), which when awakened will unite with Shiva, the supreme Hindu God, The Destroyer of Evil.  The Kundalini, when awakened, will rise up through the central nadi (energy channel) coiling through the individual chakras awakening different levels of consciousness and mystical experience until it reaches Sahasrara (Crown Chakra).  This will result in self-actualization or enlightenment.  It is said to be the awakening of inner knowledge and brings with it pure joy, pure knowledge and pure love.