Ah! The question with a dozen different answers. OK. “Celt” has come to mean several different things. There is the emic definition which is that if someone calls themselves a Celt, then they are a Celt. Due to the lack of texts we have from Iron Age peoples this is extended to mean that if a Classical author used the term Celt, then we should assume that the people they were talking about referred to themselves as Celts. Of course, this is not without its own problems, and it has been argued by Peter Wells (2001) in Beyond Celts, Germans and Scythians, that some people only called themselves Celts after the term had been applied to them by Greek and Roman authors. Thus, for the Iron Age, Celts would mean people from parts of Iberia, southern and central France, northern Italy and Bohemia. It may have been applicable to people in southern Germany and parts of the Balkans, but not the Belgae, Britons or Iron Age Irish. This becomes confusing as many people in Brittany, Scotland, Ireland, Wales, Cornwall and the Isle of Man call themselves “Celts” today, and are recognised as such by archaeologists simply because they call themselves Celts, even though their Iron Age ancestors unlikely did.
This brings us to the second part: language. A Celt is sometimes classified as someone who spoke a Celtic language. Thus, this would include peoples in Britain and Ireland, as well as the Belgae and groups like the Galatians. Now, just to be clear, nobody in antiquity used the word “Celt” to refer to language. This comes from a Welsh phenologist called Edward Lluyd who, in the 18th century, noticed that there were clear links between Welsh, Cornish, Breton and the various forms of Gaelic. Because he knew Breton pre-dated French, he decided it was the language spoken by the Celts (which was not wrong) and thus applied the term “Celtic” to describe these languages. Recently, new discoveries at the southern Spain, at the site of Tartessos, have been used to argue that the Celtic languages originated in Iberia, whereupon they spread, via trade, along the Atlantic Coast during the Bronze Age.
Then we come to the traditional definition of a Celt, based on material culture. Herodotus described how the Danube originated in the lands of the Celts. Curiously he also mentioned the Pillars of Hercules, showing that his knowledge of where the Danube originated was not fantastic (this mention of the Pillars of Hercules has recently been linked to the evidence from Tartessos). Nevertheless, in the 19th century the famous site of Hallstatt was excavated in Austria. Here a new Iron Age culture was discovered, which was named after the site. Ten years later the site of La Tène was discovered in Switzerland, and the new culture represented here was in turn named after this site. It was realised shortly after that the Hallstatt culture (c800-475BC) was succeeded in central and western Europe by the La Tène culture (c.475-20BC, on the continent). Based on Caesar’s comments that “the Gauls call themselves Celts in their own language” it was accepted that the La Tène culture was the culture of the Celts. This also fitted with the fact that the La Tène culture succeeded the Hallstatt culture, which was located at the source of the Danube at the time Herodotus had described the Celts being there. Thus, anyone who had La Tène material culture came to be viewed as a Celt. Although this covers Britain and Ireland, it doesn’t cover Iberia.
Finally, related to material culture, is art. Objects decorated in the curvilinear, abstract style of the La Tène culture are said to be decorated with “Celtic” art. Thus people talk about things like Early Medieval Irish crosses as being Celtic, when they mean the art. So, in short, there are many different ways of terming a Celt. Personally, I prefer the first option as it is more reflective of how people view themselves. It also prevents us from trying to force the archaeological record to do things it clearly can’t.
These lectures by John Collis, John Koch and Raymond Karl should help:
https://www.youtube.com/watch?v=qMmertCoa_k
https://www.youtube.com/watch?v=7aMCaoG8fMA
https://www.youtube.com/watch?v=Ub5izFOdtDs
https://www.youtube.com/watch?v=V8bU...M&t=0s&index=3