The British Museum recently opened an exhibit with considerable online tools designed to explore the very question you are asking. The issue you raise is complex, not easy to answer, and does not yield consensus. There is no question that there is a linguistic connection that tied - and to some extent still does connect - people on what has been called the Celtic Fringe. As /u/MrMedievalist points out, the term does not refer to a political entity. Indeed there never was a time when a significant majority of Celtic speakers were under a single political umbrella of their own making (the Romans imposed rule over many Celtic speakers - but that is a different story). And as /u/MrMedievalist points out, there are detractors who have been critical of the term "Celtic" and how it has mislead researchers (and more recently, Celtic enthusiasts of all types in the general public).

Your question comes as close to hinting at an answer as anyone is likely to provide. But I do suggest exploring the British Museum website. They have a great video that talks about your question - and it includes lots of wonderful images from the exhibit, so it will be more entertaining than anything written here.

edit: and by the way, you missed Cornwall (as most people usually do). I'm wrapping up the writing of a book on Cornish folklore, and I can tell you that there are many people who would have their feelings hurt because of your oversight!

It is most definitely a term used to describe cultural characteristics that define an ethnicity, so it does not refer to a political entity or any such thing. On the other hand, the very notion of "The Celts" is disputed, and regarded by its detractors as a somewhat artificial creation that misleads researchers to bundle up several disparate cultural groups under one innapropriate "catch them all" term. However, that is not my area of specialty, so I'm not very familiar with the debate. We better wait for a true expert to show up.

When people talk about things Celtic, they're usually conflating a material culture and language family into one cultural package. In reality, Celtic speakers were not required to use the associated material culture, like in Iberia, while the material culture could be used by non-Celtic speakers, which was the case in a large part of Central Europe.

It's still a contentious issue but I don't think that many Celticists would use the term 'Celtic' or 'Celt' without some sort of qualification. I'd say that there is still a use for the term, but it should only really be applied to speakers of a Celtic language regardless of their political or cultural status. Think of it like the term 'Germanic' - you could use it to refer to speakers of Danish, Old Norse, Crimean Gothic, Frankish or African-American Vernacular English, but it has no political or cultural associations beyond that.

There's actually an interesting dynamic in the Celticist world of academia: there are many people in Ireland, Wales, Brittany and Scotland who unreservedly stand by the pan-Celtic identity. Of course it's a completely modern identity with no basis in the historical past, but it's in some ways integral to how these people conceive of themselves as Irish, Welsh, Scottish etc. The contention arises when these kinds of people interact with Celticists, because they naturally take an interest in 'Celtic' history.

As I've said, most Celticists have done away with the unifying Celtic concept, and often clash with modern day self-identifying Celts who peek their heads in to glean some historical basis for their identity, only to find that the scholars committed to its study deny its existence. It's a really interesting phenomenon where the study of history/archaeology intersects with/comes into conflict with contemporary issues of identity, but in a context that isn't very racialized or colonial - these are often scholars of British or Irish heritage interacting with other people of Irish or British extraction. I'm actually planning on presenting a paper at a Celtic Studies conference that's open to the public in the winter and have to prepare in advance to handle potential 'Celts' upset with my Balkanization of the Celtic peoples (my argument is largely contingent on the uniqueness of Irish politics and society when compared to somewhere like Gaul or Britain).

Everything here is very helpful, but the one thing I haven't seen anyone talk about yet is the origin of the word. The term 'Celtic' derives from Greek and has the force of 'not-Greek' - kind of like the original meaning of the word 'barbarian' (i.e. a person who speaks a language we don't understand). Grouping them all together doesn't really tell you much more than the fact that they were all not Greeks; the linguistic and cultural differences between the various Gaulish, Britonic, and Iberian tribes in the west, as well as the Galatians as far east as Anatolia, were significant depending on where and when you're looking.

Of course there is some shared heritage between the peoples of ancient Ireland and those of Iberia, facilitated largely by the ease of seafaring, but we find many different styles of pottery from Ireland to Switzerland, and for example Gaulish and Celtiberian were distinct languages. So to answer your question: not really. We don't have to blame the Victorians - though they certainly had a hand in our current (mis)understanding - when the Greeks are at the root of it all.

Best source for everything 'Celtic': Barry Cunliffe, The Ancient Celts (OUP 1997).

All I know is that they were an extremely violent group that made the Romans fearful of them.