First, it is the music of the peoples calling themselves Celts (a non-musical, primarily political definition), as opposed to, say, "French music" or "English music." Secondly, it refers to whatever qualities may be unique to the musics of the Celtic Nations (a musical definition). Some insist that different ostensibly Celtic musics actually have nothing in common – such as Geoff Wallis and Sue Wilson in their book The Rough Guide to Irish Music – whereas others (such as Alan Stivell), say there is.
Often, the term Celtic music is applied to the music of Ireland and Scotland because both places have produced well-known distinctive styles which actually have genuine commonality and clear mutual influences; however, it is notable that Irish and Scottish traditional musicians themselves avoid the term "Celtic music," except when forced by the necessities of the market. The definition is further complicated by the fact that Irish independence has allowed Ireland to promote 'Celtic' music as a specifically Irish product. In reality, the terms 'Scots/Scottish' and 'Irish' are purely modern geographical references to a people who share a common Celtic ancestry and consequently, a common musical heritage.
These styles are known because of the importance of Irish and Scottish people in the English speaking world, especially in the United States, where they had a profound impact on American music, particularly bluegrass and country music. The music of Wales, Cornwall, the Isle of Man, Brittany, Galicia, Cantabria and Asturias (Spain) and Portugal are also considered Celtic music, the tradition being particularly strong in Brittany, where Celtic festivals large and small take place throughout the year, and in Wales, where the ancient eisteddfod tradition still occurs. Additionally, the musics of ethnically Celtic peoples abroad are vibrant, especially in Canada and the United States.