The house generally represents your psychological and emotional self. Each part of the house may deal with a different part of you. The basement is built first. It is often below ground (or at least some parts of it), and is essentially the foundation of the house. Dreaming about a basement and understanding the dream, may provide you with valuable information which may lead to greater self-awareness.
A recurring dream about basements (i.e. being in a basement, cleaning a basement, furnishing a basement, etc.) should not be ignored. These dreams may be symbolic of your unconscious, instincts and intuition, and degree of awareness of a current situation or a problem. The look of the basement may provide you with clues about your current feelings and state of contentment.
If the basement is a mess, and you see great disorder and clutter, it suggests that you may be experiencing confusion and that it is a very good time to sort things out emotionally and psychologically. At times, the activities which are going on in the basement of your dream may be based on past experiences or childhood memories. As with all dreams, their main purpose seems to be to bring the dreamer to higher consciousness so that he may deal with his current issues more effectively, rather than to dwell on the past.
See also: House.