Not much history of the knots is available prior to the beginning of the Christian influence on the Celts in about A.D. 450. There is much evidence for the use of geometrical patterns as ornamentation particularly in jewelry before that time. Some historians have theorized that early celtic religion prevented their depicting creatures realistically, similar, then, to the Islamic prohibition, which gave rise to the development of Arabic calligraphy. Still, Chinese and Japanese calligraphy seemed to arise simply from an aesthetic sense and needed no such prohibition to encourage its development.
The same pre-Christian designs found their way into early Christian manuscripts and artwork with the addition of depictions from life, such as animals, plants and even humans. In the beginning the patterns were intricately interwoven cords, called plaits, which can also be found in other areas of Europe, like Italy in 6th century. The Lindisfarne Gospels, created in northern Britain in the early 8th cent., contains the earliest example of true knotted designs in the celtic manner, with colorful and intricate illuminations.
While analysis of the knots seem to point to 8 basic types, there is no evidence to indicate that a knot had any specific philosophical or religious significance beyond perhaps the most obvious: the intricacy of God's creation and man's circuitous path through life. Modern wiccans in some covens have taken up the creation of celtic knots, attributing to them ideas and magical properties that were not there originally.
While the ancient Celts felt no need to attribute meaning to their designs, there is nothing to prevent the modern viewer from assigning signifcance. It might even be argued that from a Jungian view of the collective unconscious, that the meaning was always there but hidden during the act of creation and revealed in their contemplation.
As to their magical properties, it might be argued that creating knots is a type of yoga, where the mind is too busy with precise repetitive tasks to censor images from the unconscious. A similar set of conditions can be found in the recitation of a mantra or praying the rosary with the same kind of results.