Answer by taking a quote from the following article:

Celtic art is associated with the peoples known as Celts; those who spoke the Celtic languages in Europe from pre-history through to the modern period, as well as the art of ancient peoples whose language is uncertain, but have cultural and stylistic similarities with speakers of Celtic languages. Celtic art is a difficult term to define, covering a huge expanse of time, geography and cultures. A case has been made for artistic continuity in Europe from the Bronze Age, and indeed the preceding Neolithic age; however archaeologists generally use "Celtic" to refer to the culture of the European Iron Age from around 1000 BC onwards, until the conquest by the Roman Empire of most of the territory concerned, and art historians typically begin to talk about "Celtic art" only from the La Tene period (broadly 5th to 1st centuries BC) onwards. Early Celtic art is another term used for this period, stretching in Britain to about 150 AD.

The ancient peoples now called "Celts" spoke a group of languages that had a common origin in the Indo-European language known as Common Celtic or Proto-Celtic. This shared linguistic origin was once widely accepted by scholars to indicate peoples with a common genetic origin in southwest Europe, who had spread their culture by emigration and invasion. Archaeologists identified various cultural traits of these peoples, including styles of art, and traced the culture to the earlier Hallstatt culture and La Tene culture. More recent genetic studies have indicated that various Celtic groups do not all have shared ancestry, and have suggested a diffusion and spread of the culture without necessarily involving significant movement of peoples. The extent to which "Celtic" language, culture and genetics coincided and interacted during prehistoric periods remains very uncertain and controversial. Celtic art is associated with the peoples known as Celts; those who spoke the Celtic languages in Europe from pre-history through to the modern period, as well as the art of ancient peoples whose language is uncertain, but have cultural and stylistic similarities with speakers of Celtic languages. The term "Celt" was used in classical times as a synonym for the Gauls (Keltoi, Celtae). Its English form is modern, attested from 1607. In the late 17th century the work of scholars such as Edward Lhuyd brought academic attention to the historic links between Gaulish and the Brythonic--and Goidelic--speaking peoples, from which point the term was applied not just to continental Celts but those in Britain and Ireland. Then in the 18th century the interest in "primitivism", which led to the idea of the "noble savage", brought a wave of enthusiasm for all things Celtic and Druidic. The "Irish revival" came after the Catholic Emancipation Act of 1829 as a conscious attempt to demonstrate an Irish national identity, and with its counterpart in other countries subsequently became the "Celtic Revival".

Where does Celtic art come from?
Celtic art is associated with the peoples known as Celts;