Irish Gaelic is not the only living Celtic language. The Breton people, who live in Brittany, in the north of Europe, speak Breton, which is also Celtic.
2,000 years ago, most of the British Isles were populated by Celtic tribes. The Brythonic people (our name for them, we don't exactly know what they called themselves) lived on the southern part of Britannia, and spoke the Celtic Brythonic language. The Brythonic population got along just fine with the Roman occupiers, but when the Romans left and southern Britannia was overcome by Germanic tribes (the Angles, Saxons, Jutes, etc.), the Brythonic people saw the future and didn't like it. They pulled their boats out of storage and sailed to northwestern Europe. Their descendants are the modern Breton population in Brittany.
At this point, Britannia became Angle Land, a name which, several centuries later, was condensed into "England," and the population became primarily Germanic, as the Celtic people were left to the hinterlands.
A couple of centuries later, the Norman French invaded England, and imposed the French language on government, scholarship, religion and commerce, while the common folk continued to speak "Anglisc." This is why, to this day, we have two parallel sets of words for naming animals. The farmers spoke Anglisc and, therefore, called their animals sheep, pigs, deer, cows and chickens, while the people who dealt with the business of farming called them by French words: mutton, pork, venison, beef and cocks.
Furthermore, Welsh is also a Celtic language, spoken in Wales. However, most Welsh people speak English, and the majority cannot speak Welsh fluently--if at all.
Two other Celtic languages are still (barely) surviving. Manx is spoken by some of the inhabitants of the Isle of Man, and there is a movement to save the Cornish language, which originated in Cornwall but is now eclipsed by English.