Properly it is 'Keltic', and it applies to a wide-ranging group of tribes sharing a similar culture and similar languages. There was no united Celtic Empire or Kingdom- each tribe was a nation unto itself. They spread across Europe (originating from the Germanic forests and mountains, according to one source) and spread west and south.
The Romans called them Gauls, the Greeks Keltoi. They are supposed to have spread to Britannia, Ireland, Spain, France, northern Italy, Switzerand, the Balkans, and a few tribes ended up in central Turkey, where they became the Galatians.
In some places they became the overwhelming majority of people, as in Gaul. In others they were simply rulers, while in other areas, like Spain, they assimilated in such numbers that they changed the local population- from Iberian to Celtiberian.
Edorix will probably pop by with the details of the Celts in Britannia, so I will leave that to him.
Their main strength in dispersion was their numbers and strong tribal unity, and their internecine fighting which drove tribes to migrate. Their main weakness in dispersion was their internecine fighting which left open possibilities for 'divide and conquer' and inability to untie in the face of disaster.