Spirals are some of the oldest geometric shapes in ancient artwork dating back at least to the Neolithic period, the product of people thousands of years away from having access to writing. As such, we know very little about their religious beliefs and can, at best, guess about general meanings of symbols based on context.
Newgrange: Some of the most famous ancient spirals are at Newgrange in Ireland. Newgrange is a large mound constructed by humans with stone and earth. It was at least partially used as a tomb, but it may have had other purposes as well.
Newgrange has been hugely influential in many modern people's interpretation of spirals. Many suggest the spirals are representative of the cycle of rebirth (as indicated by their presence at a tomb) or as a symbol of a mother goddess, who in recent times has been strongly associated with underground chambers, which are interpreted as symbolic wombs.
Woman's Symbol: Because of its connection with mother goddesses, the spiral is a very feminine symbol, representing not only women but also a variety of things traditionally associated with women. Besides lifecycles, fertility and childbirth, the spiral can reference intuition and other more internal concepts associated with women.
Spirals in Nature: Spirals and circles are much more commonly found in nature than straight-edged shapes like triangles and squares. As such, people today tend to associate spirals with the natural world as opposed to the constructed, mechanical and urban world. Spirals are primal, raw, and unrestrained by man. Moreover, ancient people were acutely aware of cyclical forces of nature: monthly lunar patterns, yearly solar and seasonal patterns, which in turn affect yearly patterns in plant growth and animal husbandry. It has been suggested that at least some of the ancient spirals represent the sun, so it is sometimes described as a solar symbol. However, solar symbols are strongly male-oriented, so its use in modern beliefs is limited.
Spiral of the Cosmos: Even ancient people could recognize that the stars overhead spun around a central point every night, and today we know we reside within a spiral galaxy. Thus, the spiral can be a symbol of the universe and our place within it and of the great cycles that constantly advance within this universe. Certain spirals such as those reflecting the golden ratio (1: 1.618) or the Fibonacci sequence reflect certain mathematical truths. As such, some find those spirals to have particular value and meaning.
Symbol of Change: Life cycles and cycles of the natural world create change. The old dies away so the new can come forth. Each of us progresses from child to adult to old age. As such, the spiral is not a symbol of stagnation but rather of change, progression, and development. It embraces these things as good and healthy and helps one to accept change even though we often are more comfortable retreating into tradition and old, standard ways.
Spirals are sometimes seen as watery symbols. Water is mutable, always changing and not having permanence. It also ripples in circles. Finally, water is a feminine element along with earth. (In comparison, fire and air are masculine elements.)
-- More About Spirals --
Inner Worlds, Outer Worlds