The triple spiral or triskele is believed by many people to be an ancient symbol of pre-Celtic and Celtic beliefs. It appears in various forms in pre-Celtic and Celtic art, with the earliest examples having been found on many Irish Neolithic sites, including inside the famous Newgrange passage tomb, on the large entrance stone, and on some of the curbstones surrounding the mound. These carvings have been dated to approximately 3200 BC.
It's an ancient symbol, which is actually found in many different sites across the world.
The megalithic tomb of Newgrange in Ireland features several examples of the triple spiral. These particular examples do not feature the three-fold symmetry of later renderings but feature two intertwined spirals with the third originating from the indentation between the other two. This particular feature is rendered with high fidelity in each instance at Newgrange and would suggest a non-tripartite interpretation. One possible interpretation could be the union of male and female (the two entwined spirals) to engender an offspring though how this relates to its setting in a tomb begs explanation.
Christian Celtic Symbolism
What the symbol meant to the pagans who built Newgrange and other monuments is unknown; but, as Christianity came into the forefront in Ireland before the 5th century AD, the triskele took on new meaning, as a symbol of the Trinity (i.e., Father, Son, and Holy Spirit) and, therefore, also a symbol of eternity. Its popularity continues today as a decorative symbol of faith for Christians of Celtic descent around the world.
The triple spiral is one of the main symbols of Celtic Reconstructionist Paganism, often standing for the "three realms" - Land, Sea and Sky, or for one of a number of deities who are described in the lore as "threefold" or triadic. The god Manannán is probably most often the one symbolized by the triskele, though some also use it for the goddess Brighid. Some Celtic-inspired Wiccans also use the triple spiral symbol, most often to represent the concept of the triple goddess.
The triple spiral may represent the nine-month period of human pregnancy, since the sun takes a fourth of a year to go from the celestial equator (an equinox) to extreme north or south declination (a solstice), and vice versa. During each three-month period, the sun's path across the sky appears to form a closely wound quasi-helical shape, which can be likened to a spiral, so that three spirals could represent nine months, providing an explanation for a link between fertility and the triple-spiral symbol.