It is a trophy contested yearly by Stanford Universities and University of California american football representatives and it is regularly played since 1892.
In 1906 the Californian Universities, worried about the increased violence in american football that led in those years to many death every year, turned to rugby as the major sport, hoping to convince the East Coast Universities to follow them.
Also the Big Game turned to Rugby and the winner was invited to British Columbia every year during the Christmas holidays to play the Cooper-Keith Challenge Cup against the winner of the McKechnie Cup (the British Columbia championship).
In those years All Blacks and Wallabies toured to California while a combined American universities team toured to Australia.
After WWI, anyway, since the East Coast continued to play american football, California too returned to football and rugby was abandoned for decades.
en.wikipedia.org/wiki/1906-17_Stanford_rugby_teams - Wikipedia page about the Stanford rugby team in the period 1906 - 1917.
en.wikipedia.org/wiki/Big_Game_(American_football) - Wikipedia page about the Big Game.
Many data were found in the "Spalding Rugby Football Annual" from 1910 to 1914.