From Wikipedia:

Celtic knots are a variety of (mostly endless) knots and stylized graphical representations of knots used for decoration, adopted by the ancient Celts. Though Celtic knots were being created in Polytheistic Celtic times, these knots are most known for their adaptation for use in the ornamentation of Christian monuments and manuscripts like the 8th century Book of Kells.

History
Not much history of the knots is available before the beginning of the Christian influence on the Celts in about A.D. 450. There is much evidence for the use of geometric patterns as ornamentation particularly in jewelry before that time. Some historians have theorized that early Celtic religion prevented their depicting creatures realistically[1].

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. A fragment of a Gospel Book, now in the Durham Cathedral library and created in northern Britain in the 7th century, contains the earliest example of true knotted designs in the Celtic manner.

Examples of plaitwork (a woven, unbroken cord design) predate knotwork designs in several cultures around the world[1], but the broken and reconnected plaitwork that is characteristic of true knotwork began in Northern Italy and Southern Gaul and spread to Ireland by the 7th century[2]. The style is most commonly associated with the Celtic lands but it was also practiced extensively in England and was exported to Europe by Irish and Northumbrian monastic activities on the continent. In modern times Celtic Art is popularly thought of in terms of national identity and therefore specifically Irish, Scottish or Welsh.

Significance
J. Romilly Allen has identified "eight elementary knots which form the basis of nearly all the interlaced patterns in Celtic decorative art"[3][4]; however, there is no evidence to indicate that a knot had any specific philosophical or religious significance beyond perhaps the most obvious, that being the intricacy capable in the work of humans, itself reflective of the intricacy of Natural forms. Some Wiccans have taken up the creation of celtic knots, attributing to them ideas and magical properties that may not have been there originally.

Many items decorated with knotwork have been found in archaeological sites. Items such as torcs, bowls and cups are adorned with intricate patterns by ancient smiths.