Nobody is quite certain where the Basques originated from. Some think that they are the descendents of the original Iberians.
When the Celts first invaded Iberia, they conquered the northern half of the peninsula from present day France to Portugal. As time passed, the Basques reconquered their present territory cutting off the nortrhwestern Celts in Spain from their cousins in France.
The Celts in central Spain intermarried with the Iberians to form the Celt-Iberians encountered by the Romans. The Galician and the Asturian tribes, however, retained a purer Celtic character protected by the Cantabrian Mountains to the south and the sea to the north.
The name "Galicia" is derived from the Roman name for the region Caellecia which means "Lands of the Celts". The archeology of the period yields Celtic hill forts (Castros) and the Celtic torques common to the Celts.
Galicia was the last Celtic stronghold on the European Continent conquered by the Romans. They were not defeated until the Cantabrian War in 25 B.C. and were not fully subdued until the campaign of Augustus' general Agrippa in 19 B.C.
"Not many of the Cantabri were taken prisoner, for when they saw they had lost all hope of freedom, they lost all desire to preserve their lives either. Some set fire to their forts and cut their own throats, others willingly remained with their companions and died in the flames, while others took poison in the sight of all. In this way the great majority and the fiercest among the tribesmen were wiped out."......Cassius Dio, Roman History (XLIV.5)
"...Spain by the nature of the country and the character of its people, was better adapted than any other place in the world to making loses good for a renewal of hostilities. This is the reason why Spain, though it was the first mainland province to be entered by the Romans, was the last to be completely subdued, and held out till our own times, when it was finally conquered under the leadership and auspices of Augustus Caesar.".....The History of Rome (XXVIII.12)
Today, the national musical instrument of Galicia is the bagpipe and the dancing resembles the Irish dance.
My Y chromosome comes from Galicia. It would be interesting to see DNA studies comparing all the Celtic homelands in Europe.