This prestige event appears to have been held in a building at Pottington probably during the 19th century. The picture came to The Pilton Story archive through Terry Priscott on Facebook and depicts people, inventions and gadgets rather than livestock or produce.
However the show's origins were in agriculture, dating back to 1777, when draper, Edmund Rack, originally from Norfolk, but who moved to the City of Bath, studied modern methods for farming. He was, according to his Wikipedia entry, struck by the poor standard of agricultural practice in the West Country, and in a series of letters to the Farming Magazine and the Bath Chronicle argued that it was in the interest of all involved to make a concerted effort to improve productivity. He gained support from local philanthropists and set up a society for the encouragement of Agriculture, Planting, Manufactures, Commerce, and the Fine Arts...and specifically devoted to the improvement of animal husbandry, farm implements and country crafts through education, experimentation and prize-giving.
The society held shows across the South West, and brought its expertise to North Devon in 1859, a date you could almost guess from the hats in the picture. Any further information about the picture would be gratefully received.
Another view of the Show at Pottington in 1859 is also available on the archive at the end of this link: